category_theory.adjunction.reflective | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

239d882c

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

ee05e9ce

bump to nightly-2024-04-25-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

ad7a2212

Diff

@@ -59,7 +59,6 @@ theorem unit_obj_eq_map_unit [Reflective i] (X : C) :
 #align category_theory.unit_obj_eq_map_unit CategoryTheory.unit_obj_eq_map_unit
 -/
 
-#print CategoryTheory.isIso_unit_obj /-
 /--
 When restricted to objects in `D` given by `i : D ⥤ C`, the unit is an isomorphism. In other words,
 `η_iX` is an isomorphism for any `X` in `D`.
@@ -76,7 +75,6 @@ instance isIso_unit_obj [Reflective i] {B : D} : IsIso ((ofRightAdjoint i).Unit.
   rw [this]
   exact is_iso.inv_is_iso
 #align category_theory.is_iso_unit_obj CategoryTheory.isIso_unit_obj
--/
 
 #print CategoryTheory.Functor.essImage.unit_isIso /-
 /-- If `A` is essentially in the image of a reflective functor `i`, then `η_A` is an isomorphism.

ee05e9ce

bump to nightly-2024-04-14-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

f736ea6b

Diff

@@ -38,7 +38,8 @@ variable [Category.{v₁} C] [Category.{v₂} D] [Category.{v₃} E]
 /--
 A functor is *reflective*, or *a reflective inclusion*, if it is fully faithful and right adjoint.
 -/
-class Reflective (R : D ⥤ C) extends IsRightAdjoint R, Full R, Faithful R
+class Reflective (R : D ⥤ C) extends IsRightAdjoint R, CategoryTheory.Functor.Full R,
+    CategoryTheory.Functor.Faithful R
 #align category_theory.reflective CategoryTheory.Reflective
 -/
 
@@ -127,7 +128,7 @@ theorem mem_essImage_of_unit_isSplitMono [Reflective i] {A : C}
 #print CategoryTheory.Reflective.comp /-
 /-- Composition of reflective functors. -/
 instance Reflective.comp (F : C ⥤ D) (G : D ⥤ E) [Fr : Reflective F] [Gr : Reflective G] :
-    Reflective (F ⋙ G) where to_faithful := Faithful.comp F G
+    Reflective (F ⋙ G) where to_faithful := CategoryTheory.Functor.Faithful.comp F G
 #align category_theory.reflective.comp CategoryTheory.Reflective.comp
 -/

ee05e9ce

bump to nightly-2024-04-06-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

e34029c9

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 -/
 import CategoryTheory.Adjunction.FullyFaithful
-import CategoryTheory.Functor.ReflectsIsomorphisms
+import CategoryTheory.Functor.ReflectsIso
 import CategoryTheory.EpiMono
 
 #align_import category_theory.adjunction.reflective from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"

ee05e9ce

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -215,7 +215,7 @@ def equivEssImageOfReflective [Reflective i] : D ≌ i.EssImageSubcategory
       (by
         intro X Y f; dsimp; rw [is_iso.comp_inv_eq, assoc]
         have h := ((of_right_adjoint i).Unit.naturality f).symm
-        rw [functor.id_map] at h ; erw [← h, is_iso.inv_hom_id_assoc, functor.comp_map])
+        rw [functor.id_map] at h; erw [← h, is_iso.inv_hom_id_assoc, functor.comp_map])
 #align category_theory.equiv_ess_image_of_reflective CategoryTheory.equivEssImageOfReflective
 -/

ee05e9ce

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 -/
-import Mathbin.CategoryTheory.Adjunction.FullyFaithful
-import Mathbin.CategoryTheory.Functor.ReflectsIsomorphisms
-import Mathbin.CategoryTheory.EpiMono
+import CategoryTheory.Adjunction.FullyFaithful
+import CategoryTheory.Functor.ReflectsIsomorphisms
+import CategoryTheory.EpiMono
 
 #align_import category_theory.adjunction.reflective from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"

ee05e9ce

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.adjunction.reflective
-! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Adjunction.FullyFaithful
 import Mathbin.CategoryTheory.Functor.ReflectsIsomorphisms
 import Mathbin.CategoryTheory.EpiMono
 
+#align_import category_theory.adjunction.reflective from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
+
 /-!
 # Reflective functors

ee05e9ce

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -47,6 +47,7 @@ class Reflective (R : D ⥤ C) extends IsRightAdjoint R, Full R, Faithful R
 
 variable {i : D ⥤ C}
 
+#print CategoryTheory.unit_obj_eq_map_unit /-
 -- TODO: This holds more generally for idempotent adjunctions, not just reflective adjunctions.
 /-- For a reflective functor `i` (with left adjoint `L`), with unit `η`, we have `η_iL = iL η`.
 -/
@@ -58,7 +59,9 @@ theorem unit_obj_eq_map_unit [Reflective i] (X : C) :
     i.map_comp]
   simp
 #align category_theory.unit_obj_eq_map_unit CategoryTheory.unit_obj_eq_map_unit
+-/
 
+#print CategoryTheory.isIso_unit_obj /-
 /--
 When restricted to objects in `D` given by `i : D ⥤ C`, the unit is an isomorphism. In other words,
 `η_iX` is an isomorphism for any `X` in `D`.
@@ -75,7 +78,9 @@ instance isIso_unit_obj [Reflective i] {B : D} : IsIso ((ofRightAdjoint i).Unit.
   rw [this]
   exact is_iso.inv_is_iso
 #align category_theory.is_iso_unit_obj CategoryTheory.isIso_unit_obj
+-/
 
+#print CategoryTheory.Functor.essImage.unit_isIso /-
 /-- If `A` is essentially in the image of a reflective functor `i`, then `η_A` is an isomorphism.
 This gives that the "witness" for `A` being in the essential image can instead be given as the
 reflection of `A`, with the isomorphism as `η_A`.
@@ -95,13 +100,17 @@ theorem Functor.essImage.unit_isIso [Reflective i] {A : C} (h : A ∈ i.essImage
   rw [← nat_trans.naturality]
   simp
 #align category_theory.functor.ess_image.unit_is_iso CategoryTheory.Functor.essImage.unit_isIso
+-/
 
+#print CategoryTheory.mem_essImage_of_unit_isIso /-
 /-- If `η_A` is an isomorphism, then `A` is in the essential image of `i`. -/
 theorem mem_essImage_of_unit_isIso [IsRightAdjoint i] (A : C)
     [IsIso ((ofRightAdjoint i).Unit.app A)] : A ∈ i.essImage :=
   ⟨(leftAdjoint i).obj A, ⟨(asIso ((ofRightAdjoint i).Unit.app A)).symm⟩⟩
 #align category_theory.mem_ess_image_of_unit_is_iso CategoryTheory.mem_essImage_of_unit_isIso
+-/
 
+#print CategoryTheory.mem_essImage_of_unit_isSplitMono /-
 /-- If `η_A` is a split monomorphism, then `A` is in the reflective subcategory. -/
 theorem mem_essImage_of_unit_isSplitMono [Reflective i] {A : C}
     [IsSplitMono ((ofRightAdjoint i).Unit.app A)] : A ∈ i.essImage :=
@@ -116,6 +125,7 @@ theorem mem_essImage_of_unit_isSplitMono [Reflective i] {A : C}
   haveI := is_iso_of_epi_of_is_split_mono (η.app A)
   exact mem_ess_image_of_unit_is_iso A
 #align category_theory.mem_ess_image_of_unit_is_split_mono CategoryTheory.mem_essImage_of_unit_isSplitMono
+-/
 
 #print CategoryTheory.Reflective.comp /-
 /-- Composition of reflective functors. -/
@@ -124,19 +134,24 @@ instance Reflective.comp (F : C ⥤ D) (G : D ⥤ E) [Fr : Reflective F] [Gr : R
 #align category_theory.reflective.comp CategoryTheory.Reflective.comp
 -/
 
+#print CategoryTheory.unitCompPartialBijectiveAux /-
 /-- (Implementation) Auxiliary definition for `unit_comp_partial_bijective`. -/
 def unitCompPartialBijectiveAux [Reflective i] (A : C) (B : D) :
     (A ⟶ i.obj B) ≃ (i.obj ((leftAdjoint i).obj A) ⟶ i.obj B) :=
   ((Adjunction.ofRightAdjoint i).homEquiv _ _).symm.trans (equivOfFullyFaithful i)
 #align category_theory.unit_comp_partial_bijective_aux CategoryTheory.unitCompPartialBijectiveAux
+-/
 
+#print CategoryTheory.unitCompPartialBijectiveAux_symm_apply /-
 /-- The description of the inverse of the bijection `unit_comp_partial_bijective_aux`. -/
 theorem unitCompPartialBijectiveAux_symm_apply [Reflective i] {A : C} {B : D}
     (f : i.obj ((leftAdjoint i).obj A) ⟶ i.obj B) :
     (unitCompPartialBijectiveAux _ _).symm f = (ofRightAdjoint i).Unit.app A ≫ f := by
   simp [unit_comp_partial_bijective_aux]
 #align category_theory.unit_comp_partial_bijective_aux_symm_apply CategoryTheory.unitCompPartialBijectiveAux_symm_apply
+-/
 
+#print CategoryTheory.unitCompPartialBijective /-
 /-- If `i` has a reflector `L`, then the function `(i.obj (L.obj A) ⟶ B) → (A ⟶ B)` given by
 precomposing with `η.app A` is a bijection provided `B` is in the essential image of `i`.
 That is, the function `λ (f : i.obj (L.obj A) ⟶ B), η.app A ≫ f` is bijective, as long as `B` is in
@@ -155,25 +170,33 @@ def unitCompPartialBijective [Reflective i] (A : C) {B : C} (hB : B ∈ i.essIma
     _ ≃ (i.obj _ ⟶ i.obj hB.witness) := (unitCompPartialBijectiveAux _ _)
     _ ≃ (i.obj ((leftAdjoint i).obj A) ⟶ B) := Iso.homCongr (Iso.refl _) hB.getIso
 #align category_theory.unit_comp_partial_bijective CategoryTheory.unitCompPartialBijective
+-/
 
+#print CategoryTheory.unitCompPartialBijective_symm_apply /-
 @[simp]
 theorem unitCompPartialBijective_symm_apply [Reflective i] (A : C) {B : C} (hB : B ∈ i.essImage)
     (f) : (unitCompPartialBijective A hB).symm f = (ofRightAdjoint i).Unit.app A ≫ f := by
   simp [unit_comp_partial_bijective, unit_comp_partial_bijective_aux_symm_apply]
 #align category_theory.unit_comp_partial_bijective_symm_apply CategoryTheory.unitCompPartialBijective_symm_apply
+-/
 
+#print CategoryTheory.unitCompPartialBijective_symm_natural /-
 theorem unitCompPartialBijective_symm_natural [Reflective i] (A : C) {B B' : C} (h : B ⟶ B')
     (hB : B ∈ i.essImage) (hB' : B' ∈ i.essImage) (f : i.obj ((leftAdjoint i).obj A) ⟶ B) :
     (unitCompPartialBijective A hB').symm (f ≫ h) = (unitCompPartialBijective A hB).symm f ≫ h := by
   simp
 #align category_theory.unit_comp_partial_bijective_symm_natural CategoryTheory.unitCompPartialBijective_symm_natural
+-/
 
+#print CategoryTheory.unitCompPartialBijective_natural /-
 theorem unitCompPartialBijective_natural [Reflective i] (A : C) {B B' : C} (h : B ⟶ B')
     (hB : B ∈ i.essImage) (hB' : B' ∈ i.essImage) (f : A ⟶ B) :
     (unitCompPartialBijective A hB') (f ≫ h) = unitCompPartialBijective A hB f ≫ h := by
   rw [← Equiv.eq_symm_apply, unit_comp_partial_bijective_symm_natural A h, Equiv.symm_apply_apply]
 #align category_theory.unit_comp_partial_bijective_natural CategoryTheory.unitCompPartialBijective_natural
+-/
 
+#print CategoryTheory.equivEssImageOfReflective /-
 /-- If `i : D ⥤ C` is reflective, the inverse functor of `i ≌ F.ess_image` can be explicitly
 defined by the reflector. -/
 @[simps]
@@ -197,6 +220,7 @@ def equivEssImageOfReflective [Reflective i] : D ≌ i.EssImageSubcategory
         have h := ((of_right_adjoint i).Unit.naturality f).symm
         rw [functor.id_map] at h ; erw [← h, is_iso.inv_hom_id_assoc, functor.comp_map])
 #align category_theory.equiv_ess_image_of_reflective CategoryTheory.equivEssImageOfReflective
+-/
 
 end CategoryTheory

ee05e9ce

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -154,7 +154,6 @@ def unitCompPartialBijective [Reflective i] (A : C) {B : C} (hB : B ∈ i.essIma
     (A ⟶ B) ≃ (A ⟶ i.obj hB.witness) := Iso.homCongr (Iso.refl _) hB.getIso.symm
     _ ≃ (i.obj _ ⟶ i.obj hB.witness) := (unitCompPartialBijectiveAux _ _)
     _ ≃ (i.obj ((leftAdjoint i).obj A) ⟶ B) := Iso.homCongr (Iso.refl _) hB.getIso
-    
 #align category_theory.unit_comp_partial_bijective CategoryTheory.unitCompPartialBijective
 
 @[simp]

ee05e9ce

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -196,7 +196,7 @@ def equivEssImageOfReflective [Reflective i] : D ≌ i.EssImageSubcategory
       (by
         intro X Y f; dsimp; rw [is_iso.comp_inv_eq, assoc]
         have h := ((of_right_adjoint i).Unit.naturality f).symm
-        rw [functor.id_map] at h; erw [← h, is_iso.inv_hom_id_assoc, functor.comp_map])
+        rw [functor.id_map] at h ; erw [← h, is_iso.inv_hom_id_assoc, functor.comp_map])
 #align category_theory.equiv_ess_image_of_reflective CategoryTheory.equivEssImageOfReflective
 
 end CategoryTheory

ee05e9ce

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -47,9 +47,6 @@ class Reflective (R : D ⥤ C) extends IsRightAdjoint R, Full R, Faithful R
 
 variable {i : D ⥤ C}
 
-/- warning: category_theory.unit_obj_eq_map_unit -> CategoryTheory.unit_obj_eq_map_unit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.unit_obj_eq_map_unit CategoryTheory.unit_obj_eq_map_unitₓ'. -/
 -- TODO: This holds more generally for idempotent adjunctions, not just reflective adjunctions.
 /-- For a reflective functor `i` (with left adjoint `L`), with unit `η`, we have `η_iL = iL η`.
 -/
@@ -62,12 +59,6 @@ theorem unit_obj_eq_map_unit [Reflective i] (X : C) :
   simp
 #align category_theory.unit_obj_eq_map_unit CategoryTheory.unit_obj_eq_map_unit
 
-/- warning: category_theory.is_iso_unit_obj -> CategoryTheory.isIso_unit_obj is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {B : D}, CategoryTheory.IsIso.{u1, u3} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {B : D}, CategoryTheory.IsIso.{u1, u3} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))
-Case conversion may be inaccurate. Consider using '#align category_theory.is_iso_unit_obj CategoryTheory.isIso_unit_objₓ'. -/
 /--
 When restricted to objects in `D` given by `i : D ⥤ C`, the unit is an isomorphism. In other words,
 `η_iX` is an isomorphism for any `X` in `D`.
@@ -85,12 +76,6 @@ instance isIso_unit_obj [Reflective i] {B : D} : IsIso ((ofRightAdjoint i).Unit.
   exact is_iso.inv_is_iso
 #align category_theory.is_iso_unit_obj CategoryTheory.isIso_unit_obj
 
-/- warning: category_theory.functor.ess_image.unit_is_iso -> CategoryTheory.Functor.essImage.unit_isIso is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C}, (Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) A (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) -> (CategoryTheory.IsIso.{u1, u3} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) A) (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) A) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A))
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C}, (Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) A (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) -> (CategoryTheory.IsIso.{u1, u3} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A))
-Case conversion may be inaccurate. Consider using '#align category_theory.functor.ess_image.unit_is_iso CategoryTheory.Functor.essImage.unit_isIsoₓ'. -/
 /-- If `A` is essentially in the image of a reflective functor `i`, then `η_A` is an isomorphism.
 This gives that the "witness" for `A` being in the essential image can instead be given as the
 reflection of `A`, with the isomorphism as `η_A`.
@@ -111,24 +96,12 @@ theorem Functor.essImage.unit_isIso [Reflective i] {A : C} (h : A ∈ i.essImage
   simp
 #align category_theory.functor.ess_image.unit_is_iso CategoryTheory.Functor.essImage.unit_isIso
 
-/- warning: category_theory.mem_ess_image_of_unit_is_iso -> CategoryTheory.mem_essImage_of_unit_isIso is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.IsRightAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i] (A : C) [_inst_5 : CategoryTheory.IsIso.{u1, u3} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) A) (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i _inst_4) i) A) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i _inst_4) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i _inst_4) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i _inst_4)) A)], Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) A (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.IsRightAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i] (A : C) [_inst_5 : CategoryTheory.IsIso.{u1, u3} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i _inst_4) i)) A) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i _inst_4) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i _inst_4) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i _inst_4)) A)], Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) A (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)
-Case conversion may be inaccurate. Consider using '#align category_theory.mem_ess_image_of_unit_is_iso CategoryTheory.mem_essImage_of_unit_isIsoₓ'. -/
 /-- If `η_A` is an isomorphism, then `A` is in the essential image of `i`. -/
 theorem mem_essImage_of_unit_isIso [IsRightAdjoint i] (A : C)
     [IsIso ((ofRightAdjoint i).Unit.app A)] : A ∈ i.essImage :=
   ⟨(leftAdjoint i).obj A, ⟨(asIso ((ofRightAdjoint i).Unit.app A)).symm⟩⟩
 #align category_theory.mem_ess_image_of_unit_is_iso CategoryTheory.mem_essImage_of_unit_isIso
 
-/- warning: category_theory.mem_ess_image_of_unit_is_split_mono -> CategoryTheory.mem_essImage_of_unit_isSplitMono is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C} [_inst_5 : CategoryTheory.IsSplitMono.{u1, u3} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) A) (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) A) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)], Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) A (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C} [_inst_5 : CategoryTheory.IsSplitMono.{u1, u3} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)], Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) A (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)
-Case conversion may be inaccurate. Consider using '#align category_theory.mem_ess_image_of_unit_is_split_mono CategoryTheory.mem_essImage_of_unit_isSplitMonoₓ'. -/
 /-- If `η_A` is a split monomorphism, then `A` is in the reflective subcategory. -/
 theorem mem_essImage_of_unit_isSplitMono [Reflective i] {A : C}
     [IsSplitMono ((ofRightAdjoint i).Unit.app A)] : A ∈ i.essImage :=
@@ -151,21 +124,12 @@ instance Reflective.comp (F : C ⥤ D) (G : D ⥤ E) [Fr : Reflective F] [Gr : R
 #align category_theory.reflective.comp CategoryTheory.Reflective.comp
 -/
 
-/- warning: category_theory.unit_comp_partial_bijective_aux -> CategoryTheory.unitCompPartialBijectiveAux is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) (B : D), Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) (B : D), Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))
-Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_aux CategoryTheory.unitCompPartialBijectiveAuxₓ'. -/
 /-- (Implementation) Auxiliary definition for `unit_comp_partial_bijective`. -/
 def unitCompPartialBijectiveAux [Reflective i] (A : C) (B : D) :
     (A ⟶ i.obj B) ≃ (i.obj ((leftAdjoint i).obj A) ⟶ i.obj B) :=
   ((Adjunction.ofRightAdjoint i).homEquiv _ _).symm.trans (equivOfFullyFaithful i)
 #align category_theory.unit_comp_partial_bijective_aux CategoryTheory.unitCompPartialBijectiveAux
 
-/- warning: category_theory.unit_comp_partial_bijective_aux_symm_apply -> CategoryTheory.unitCompPartialBijectiveAux_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_aux_symm_apply CategoryTheory.unitCompPartialBijectiveAux_symm_applyₓ'. -/
 /-- The description of the inverse of the bijection `unit_comp_partial_bijective_aux`. -/
 theorem unitCompPartialBijectiveAux_symm_apply [Reflective i] {A : C} {B : D}
     (f : i.obj ((leftAdjoint i).obj A) ⟶ i.obj B) :
@@ -173,12 +137,6 @@ theorem unitCompPartialBijectiveAux_symm_apply [Reflective i] {A : C} {B : D}
   simp [unit_comp_partial_bijective_aux]
 #align category_theory.unit_comp_partial_bijective_aux_symm_apply CategoryTheory.unitCompPartialBijectiveAux_symm_apply
 
-/- warning: category_theory.unit_comp_partial_bijective -> CategoryTheory.unitCompPartialBijective is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C}, (Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) -> (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B))
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C}, (Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) -> (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B))
-Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective CategoryTheory.unitCompPartialBijectiveₓ'. -/
 /-- If `i` has a reflector `L`, then the function `(i.obj (L.obj A) ⟶ B) → (A ⟶ B)` given by
 precomposing with `η.app A` is a bijection provided `B` is in the essential image of `i`.
 That is, the function `λ (f : i.obj (L.obj A) ⟶ B), η.app A ≫ f` is bijective, as long as `B` is in
@@ -199,39 +157,24 @@ def unitCompPartialBijective [Reflective i] (A : C) {B : C} (hB : B ∈ i.essIma
     
 #align category_theory.unit_comp_partial_bijective CategoryTheory.unitCompPartialBijective
 
-/- warning: category_theory.unit_comp_partial_bijective_symm_apply -> CategoryTheory.unitCompPartialBijective_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_symm_apply CategoryTheory.unitCompPartialBijective_symm_applyₓ'. -/
 @[simp]
 theorem unitCompPartialBijective_symm_apply [Reflective i] (A : C) {B : C} (hB : B ∈ i.essImage)
     (f) : (unitCompPartialBijective A hB).symm f = (ofRightAdjoint i).Unit.app A ≫ f := by
   simp [unit_comp_partial_bijective, unit_comp_partial_bijective_aux_symm_apply]
 #align category_theory.unit_comp_partial_bijective_symm_apply CategoryTheory.unitCompPartialBijective_symm_apply
 
-/- warning: category_theory.unit_comp_partial_bijective_symm_natural -> CategoryTheory.unitCompPartialBijective_symm_natural is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_symm_natural CategoryTheory.unitCompPartialBijective_symm_naturalₓ'. -/
 theorem unitCompPartialBijective_symm_natural [Reflective i] (A : C) {B B' : C} (h : B ⟶ B')
     (hB : B ∈ i.essImage) (hB' : B' ∈ i.essImage) (f : i.obj ((leftAdjoint i).obj A) ⟶ B) :
     (unitCompPartialBijective A hB').symm (f ≫ h) = (unitCompPartialBijective A hB).symm f ≫ h := by
   simp
 #align category_theory.unit_comp_partial_bijective_symm_natural CategoryTheory.unitCompPartialBijective_symm_natural
 
-/- warning: category_theory.unit_comp_partial_bijective_natural -> CategoryTheory.unitCompPartialBijective_natural is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_natural CategoryTheory.unitCompPartialBijective_naturalₓ'. -/
 theorem unitCompPartialBijective_natural [Reflective i] (A : C) {B B' : C} (h : B ⟶ B')
     (hB : B ∈ i.essImage) (hB' : B' ∈ i.essImage) (f : A ⟶ B) :
     (unitCompPartialBijective A hB') (f ≫ h) = unitCompPartialBijective A hB f ≫ h := by
   rw [← Equiv.eq_symm_apply, unit_comp_partial_bijective_symm_natural A h, Equiv.symm_apply_apply]
 #align category_theory.unit_comp_partial_bijective_natural CategoryTheory.unitCompPartialBijective_natural
 
-/- warning: category_theory.equiv_ess_image_of_reflective -> CategoryTheory.equivEssImageOfReflective is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i], CategoryTheory.Equivalence.{u2, u1, u4, u3} D _inst_2 (CategoryTheory.Functor.EssImageSubcategory.{u2, u1, u4, u3} D C _inst_2 _inst_1 i) (CategoryTheory.Functor.EssImageSubcategory.category.{u1, u3, u4, u2} D C _inst_2 _inst_1 i)
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i], CategoryTheory.Equivalence.{u2, u1, u4, u3} D (CategoryTheory.Functor.EssImageSubcategory.{u2, u1, u4, u3} D C _inst_2 _inst_1 i) _inst_2 (CategoryTheory.Functor.instCategoryEssImageSubcategory.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)
-Case conversion may be inaccurate. Consider using '#align category_theory.equiv_ess_image_of_reflective CategoryTheory.equivEssImageOfReflectiveₓ'. -/
 /-- If `i : D ⥤ C` is reflective, the inverse functor of `i ≌ F.ess_image` can be explicitly
 defined by the reflector. -/
 @[simps]

ee05e9ce

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -242,24 +242,18 @@ def equivEssImageOfReflective [Reflective i] : D ≌ i.EssImageSubcategory
   unitIso :=
     NatIso.ofComponents (fun X => (asIso <| (ofRightAdjoint i).counit.app X).symm)
       (by
-        intro X Y f
-        dsimp
-        simp only [is_iso.eq_inv_comp, is_iso.comp_inv_eq, category.assoc]
+        intro X Y f; dsimp; simp only [is_iso.eq_inv_comp, is_iso.comp_inv_eq, category.assoc]
         exact ((of_right_adjoint i).counit.naturality _).symm)
   counitIso :=
     NatIso.ofComponents
       (fun X => by
-        refine' iso.symm <| as_iso _
-        exact (of_right_adjoint i).Unit.app X.obj
+        refine' iso.symm <| as_iso _; exact (of_right_adjoint i).Unit.app X.obj
         apply (config := { instances := false }) is_iso_of_reflects_iso _ i.ess_image_inclusion
         exact functor.ess_image.unit_is_iso X.property)
       (by
-        intro X Y f
-        dsimp
-        rw [is_iso.comp_inv_eq, assoc]
+        intro X Y f; dsimp; rw [is_iso.comp_inv_eq, assoc]
         have h := ((of_right_adjoint i).Unit.naturality f).symm
-        rw [functor.id_map] at h
-        erw [← h, is_iso.inv_hom_id_assoc, functor.comp_map])
+        rw [functor.id_map] at h; erw [← h, is_iso.inv_hom_id_assoc, functor.comp_map])
 #align category_theory.equiv_ess_image_of_reflective CategoryTheory.equivEssImageOfReflective
 
 end CategoryTheory

ee05e9ce

bump to nightly-2023-05-28-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6c6011cf

Diff

@@ -48,10 +48,7 @@ class Reflective (R : D ⥤ C) extends IsRightAdjoint R, Full R, Faithful R
 variable {i : D ⥤ C}
 
 /- warning: category_theory.unit_obj_eq_map_unit -> CategoryTheory.unit_obj_eq_map_unit is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (X : C), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) X))) (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) X)))) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) X))) (CategoryTheory.Functor.map.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) X))) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) X (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) X)) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) X)))
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (X : C), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) X))) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) X)))) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) X))) (Prefunctor.map.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) X)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) X)) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) X) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) X) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) X)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.unit_obj_eq_map_unit CategoryTheory.unit_obj_eq_map_unitₓ'. -/
 -- TODO: This holds more generally for idempotent adjunctions, not just reflective adjunctions.
 /-- For a reflective functor `i` (with left adjoint `L`), with unit `η`, we have `η_iL = iL η`.
@@ -167,10 +164,7 @@ def unitCompPartialBijectiveAux [Reflective i] (A : C) (B : D) :
 #align category_theory.unit_comp_partial_bijective_aux CategoryTheory.unitCompPartialBijectiveAux
 
 /- warning: category_theory.unit_comp_partial_bijective_aux_symm_apply -> CategoryTheory.unitCompPartialBijectiveAux_symm_apply is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C} {B : D} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (CategoryTheory.unitCompPartialBijectiveAux.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) A) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C} {B : D} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (CategoryTheory.unitCompPartialBijectiveAux.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_aux_symm_apply CategoryTheory.unitCompPartialBijectiveAux_symm_applyₓ'. -/
 /-- The description of the inverse of the bijection `unit_comp_partial_bijective_aux`. -/
 theorem unitCompPartialBijectiveAux_symm_apply [Reflective i] {A : C} {B : D}
@@ -206,10 +200,7 @@ def unitCompPartialBijective [Reflective i] (A : C) {B : C} (hB : B ∈ i.essIma
 #align category_theory.unit_comp_partial_bijective CategoryTheory.unitCompPartialBijective
 
 /- warning: category_theory.unit_comp_partial_bijective_symm_apply -> CategoryTheory.unitCompPartialBijective_symm_apply is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} (hB : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) A) B (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) f) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) B (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_symm_apply CategoryTheory.unitCompPartialBijective_symm_applyₓ'. -/
 @[simp]
 theorem unitCompPartialBijective_symm_apply [Reflective i] (A : C) {B : C} (hB : B ∈ i.essImage)
@@ -218,10 +209,7 @@ theorem unitCompPartialBijective_symm_apply [Reflective i] (A : C) {B : C} (hB :
 #align category_theory.unit_comp_partial_bijective_symm_apply CategoryTheory.unitCompPartialBijective_symm_apply
 
 /- warning: category_theory.unit_comp_partial_bijective_symm_natural -> CategoryTheory.unitCompPartialBijective_symm_natural is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB')) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) h)
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' f h)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB')) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) h)
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_symm_natural CategoryTheory.unitCompPartialBijective_symm_naturalₓ'. -/
 theorem unitCompPartialBijective_symm_natural [Reflective i] (A : C) {B B' : C} (h : B ⟶ B')
     (hB : B ∈ i.essImage) (hB' : B' ∈ i.essImage) (f : i.obj ((leftAdjoint i).obj A) ⟶ B) :
@@ -230,10 +218,7 @@ theorem unitCompPartialBijective_symm_natural [Reflective i] (A : C) {B B' : C}
 #align category_theory.unit_comp_partial_bijective_symm_natural CategoryTheory.unitCompPartialBijective_symm_natural
 
 /- warning: category_theory.unit_comp_partial_bijective_natural -> CategoryTheory.unitCompPartialBijective_natural is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B B' (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB) f) h)
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B')) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B')) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B)) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB) f) h)
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_natural CategoryTheory.unitCompPartialBijective_naturalₓ'. -/
 theorem unitCompPartialBijective_natural [Reflective i] (A : C) {B B' : C} (h : B ⟶ B')
     (hB : B ∈ i.essImage) (hB' : B' ∈ i.essImage) (f : A ⟶ B) :

ee05e9ce

bump to nightly-2023-05-19-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

a31df521

Diff

@@ -170,7 +170,7 @@ def unitCompPartialBijectiveAux [Reflective i] (A : C) (B : D) :
 lean 3 declaration is
   forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C} {B : D} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (CategoryTheory.unitCompPartialBijectiveAux.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) A) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
 but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C} {B : D} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (CategoryTheory.unitCompPartialBijectiveAux.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C} {B : D} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (CategoryTheory.unitCompPartialBijectiveAux.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
 Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_aux_symm_apply CategoryTheory.unitCompPartialBijectiveAux_symm_applyₓ'. -/
 /-- The description of the inverse of the bijection `unit_comp_partial_bijective_aux`. -/
 theorem unitCompPartialBijectiveAux_symm_apply [Reflective i] {A : C} {B : D}
@@ -209,7 +209,7 @@ def unitCompPartialBijective [Reflective i] (A : C) {B : C} (hB : B ∈ i.essIma
 lean 3 declaration is
   forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} (hB : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) A) B (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
 but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) f) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) B (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) f) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) B (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
 Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_symm_apply CategoryTheory.unitCompPartialBijective_symm_applyₓ'. -/
 @[simp]
 theorem unitCompPartialBijective_symm_apply [Reflective i] (A : C) {B : C} (hB : B ∈ i.essImage)
@@ -221,7 +221,7 @@ theorem unitCompPartialBijective_symm_apply [Reflective i] (A : C) {B : C} (hB :
 lean 3 declaration is
   forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB')) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) h)
 but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' f h)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB')) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) h)
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' f h)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB')) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) h)
 Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_symm_natural CategoryTheory.unitCompPartialBijective_symm_naturalₓ'. -/
 theorem unitCompPartialBijective_symm_natural [Reflective i] (A : C) {B B' : C} (h : B ⟶ B')
     (hB : B ∈ i.essImage) (hB' : B' ∈ i.essImage) (f : i.obj ((leftAdjoint i).obj A) ⟶ B) :
@@ -233,7 +233,7 @@ theorem unitCompPartialBijective_symm_natural [Reflective i] (A : C) {B B' : C}
 lean 3 declaration is
   forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B B' (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB) f) h)
 but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B')) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B')) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B)) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB) f) h)
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B')) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B')) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B)) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB) f) h)
 Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_natural CategoryTheory.unitCompPartialBijective_naturalₓ'. -/
 theorem unitCompPartialBijective_natural [Reflective i] (A : C) {B B' : C} (h : B ⟶ B')
     (hB : B ∈ i.essImage) (hB' : B' ∈ i.essImage) (f : A ⟶ B) :

ee05e9ce

bump to nightly-2023-03-11-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

a8ee822f

Diff

@@ -170,7 +170,7 @@ def unitCompPartialBijectiveAux [Reflective i] (A : C) (B : D) :
 lean 3 declaration is
   forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C} {B : D} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (CategoryTheory.unitCompPartialBijectiveAux.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) A) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
 but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C} {B : D} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (CategoryTheory.unitCompPartialBijectiveAux.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C} {B : D} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (CategoryTheory.unitCompPartialBijectiveAux.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
 Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_aux_symm_apply CategoryTheory.unitCompPartialBijectiveAux_symm_applyₓ'. -/
 /-- The description of the inverse of the bijection `unit_comp_partial_bijective_aux`. -/
 theorem unitCompPartialBijectiveAux_symm_apply [Reflective i] {A : C} {B : D}
@@ -209,7 +209,7 @@ def unitCompPartialBijective [Reflective i] (A : C) {B : C} (hB : B ∈ i.essIma
 lean 3 declaration is
   forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} (hB : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) A) B (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
 but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) f) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) B (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) f) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) B (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
 Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_symm_apply CategoryTheory.unitCompPartialBijective_symm_applyₓ'. -/
 @[simp]
 theorem unitCompPartialBijective_symm_apply [Reflective i] (A : C) {B : C} (hB : B ∈ i.essImage)
@@ -221,7 +221,7 @@ theorem unitCompPartialBijective_symm_apply [Reflective i] (A : C) {B : C} (hB :
 lean 3 declaration is
   forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB')) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) h)
 but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' f h)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB')) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) h)
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' f h)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB')) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) h)
 Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_symm_natural CategoryTheory.unitCompPartialBijective_symm_naturalₓ'. -/
 theorem unitCompPartialBijective_symm_natural [Reflective i] (A : C) {B B' : C} (h : B ⟶ B')
     (hB : B ∈ i.essImage) (hB' : B' ∈ i.essImage) (f : i.obj ((leftAdjoint i).obj A) ⟶ B) :
@@ -233,7 +233,7 @@ theorem unitCompPartialBijective_symm_natural [Reflective i] (A : C) {B B' : C}
 lean 3 declaration is
   forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B B' (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB) f) h)
 but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B')) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B')) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B)) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB) f) h)
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B')) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B')) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B)) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB) f) h)
 Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_natural CategoryTheory.unitCompPartialBijective_naturalₓ'. -/
 theorem unitCompPartialBijective_natural [Reflective i] (A : C) {B B' : C} (h : B ⟶ B')
     (hB : B ∈ i.essImage) (hB' : B' ∈ i.essImage) (f : A ⟶ B) :

ee05e9ce

bump to nightly-2023-03-02-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

db7421c3

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 
 ! This file was ported from Lean 3 source module category_theory.adjunction.reflective
-! leanprover-community/mathlib commit 239d882c4fb58361ee8b3b39fb2091320edef10a
+! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.CategoryTheory.EpiMono
 /-!
 # Reflective functors
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Basic properties of reflective functors, especially those relating to their essential image.
 
 Note properties of reflective functors relating to limits and colimits are included in

239d882c

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -197,7 +197,7 @@ def unitCompPartialBijective [Reflective i] (A : C) {B : C} (hB : B ∈ i.essIma
     (A ⟶ B) ≃ (i.obj ((leftAdjoint i).obj A) ⟶ B) :=
   calc
     (A ⟶ B) ≃ (A ⟶ i.obj hB.witness) := Iso.homCongr (Iso.refl _) hB.getIso.symm
-    _ ≃ (i.obj _ ⟶ i.obj hB.witness) := unitCompPartialBijectiveAux _ _
+    _ ≃ (i.obj _ ⟶ i.obj hB.witness) := (unitCompPartialBijectiveAux _ _)
     _ ≃ (i.obj ((leftAdjoint i).obj A) ⟶ B) := Iso.homCongr (Iso.refl _) hB.getIso
     
 #align category_theory.unit_comp_partial_bijective CategoryTheory.unitCompPartialBijective

239d882c

bump to nightly-2023-02-25-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49

aca219f8

Diff

@@ -34,14 +34,22 @@ variable {C : Type u₁} {D : Type u₂} {E : Type u₃}
 
 variable [Category.{v₁} C] [Category.{v₂} D] [Category.{v₃} E]
 
+#print CategoryTheory.Reflective /-
 /--
 A functor is *reflective*, or *a reflective inclusion*, if it is fully faithful and right adjoint.
 -/
 class Reflective (R : D ⥤ C) extends IsRightAdjoint R, Full R, Faithful R
 #align category_theory.reflective CategoryTheory.Reflective
+-/
 
 variable {i : D ⥤ C}
 
+/- warning: category_theory.unit_obj_eq_map_unit -> CategoryTheory.unit_obj_eq_map_unit is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (X : C), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) X))) (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) X)))) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) X))) (CategoryTheory.Functor.map.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) X))) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) X (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) X)) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) X)))
+but is expected to have type
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (X : C), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) X))) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) X)))) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) X))) (Prefunctor.map.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) X)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) X)) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) X) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) X) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) X)))
+Case conversion may be inaccurate. Consider using '#align category_theory.unit_obj_eq_map_unit CategoryTheory.unit_obj_eq_map_unitₓ'. -/
 -- TODO: This holds more generally for idempotent adjunctions, not just reflective adjunctions.
 /-- For a reflective functor `i` (with left adjoint `L`), with unit `η`, we have `η_iL = iL η`.
 -/
@@ -54,6 +62,12 @@ theorem unit_obj_eq_map_unit [Reflective i] (X : C) :
   simp
 #align category_theory.unit_obj_eq_map_unit CategoryTheory.unit_obj_eq_map_unit
 
+/- warning: category_theory.is_iso_unit_obj -> CategoryTheory.isIso_unit_obj is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {B : D}, CategoryTheory.IsIso.{u1, u3} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))
+but is expected to have type
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {B : D}, CategoryTheory.IsIso.{u1, u3} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))
+Case conversion may be inaccurate. Consider using '#align category_theory.is_iso_unit_obj CategoryTheory.isIso_unit_objₓ'. -/
 /--
 When restricted to objects in `D` given by `i : D ⥤ C`, the unit is an isomorphism. In other words,
 `η_iX` is an isomorphism for any `X` in `D`.
@@ -71,6 +85,12 @@ instance isIso_unit_obj [Reflective i] {B : D} : IsIso ((ofRightAdjoint i).Unit.
   exact is_iso.inv_is_iso
 #align category_theory.is_iso_unit_obj CategoryTheory.isIso_unit_obj
 
+/- warning: category_theory.functor.ess_image.unit_is_iso -> CategoryTheory.Functor.essImage.unit_isIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C}, (Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) A (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) -> (CategoryTheory.IsIso.{u1, u3} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) A) (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) A) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A))
+but is expected to have type
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C}, (Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) A (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) -> (CategoryTheory.IsIso.{u1, u3} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A))
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.ess_image.unit_is_iso CategoryTheory.Functor.essImage.unit_isIsoₓ'. -/
 /-- If `A` is essentially in the image of a reflective functor `i`, then `η_A` is an isomorphism.
 This gives that the "witness" for `A` being in the essential image can instead be given as the
 reflection of `A`, with the isomorphism as `η_A`.
@@ -91,12 +111,24 @@ theorem Functor.essImage.unit_isIso [Reflective i] {A : C} (h : A ∈ i.essImage
   simp
 #align category_theory.functor.ess_image.unit_is_iso CategoryTheory.Functor.essImage.unit_isIso
 
+/- warning: category_theory.mem_ess_image_of_unit_is_iso -> CategoryTheory.mem_essImage_of_unit_isIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.IsRightAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i] (A : C) [_inst_5 : CategoryTheory.IsIso.{u1, u3} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) A) (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i _inst_4) i) A) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i _inst_4) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i _inst_4) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i _inst_4)) A)], Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) A (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)
+but is expected to have type
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.IsRightAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i] (A : C) [_inst_5 : CategoryTheory.IsIso.{u1, u3} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i _inst_4) i)) A) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i _inst_4) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i _inst_4) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i _inst_4)) A)], Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) A (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)
+Case conversion may be inaccurate. Consider using '#align category_theory.mem_ess_image_of_unit_is_iso CategoryTheory.mem_essImage_of_unit_isIsoₓ'. -/
 /-- If `η_A` is an isomorphism, then `A` is in the essential image of `i`. -/
 theorem mem_essImage_of_unit_isIso [IsRightAdjoint i] (A : C)
     [IsIso ((ofRightAdjoint i).Unit.app A)] : A ∈ i.essImage :=
   ⟨(leftAdjoint i).obj A, ⟨(asIso ((ofRightAdjoint i).Unit.app A)).symm⟩⟩
 #align category_theory.mem_ess_image_of_unit_is_iso CategoryTheory.mem_essImage_of_unit_isIso
 
+/- warning: category_theory.mem_ess_image_of_unit_is_split_mono -> CategoryTheory.mem_essImage_of_unit_isSplitMono is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C} [_inst_5 : CategoryTheory.IsSplitMono.{u1, u3} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) A) (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) A) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)], Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) A (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)
+but is expected to have type
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C} [_inst_5 : CategoryTheory.IsSplitMono.{u1, u3} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)], Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) A (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)
+Case conversion may be inaccurate. Consider using '#align category_theory.mem_ess_image_of_unit_is_split_mono CategoryTheory.mem_essImage_of_unit_isSplitMonoₓ'. -/
 /-- If `η_A` is a split monomorphism, then `A` is in the reflective subcategory. -/
 theorem mem_essImage_of_unit_isSplitMono [Reflective i] {A : C}
     [IsSplitMono ((ofRightAdjoint i).Unit.app A)] : A ∈ i.essImage :=
@@ -112,17 +144,31 @@ theorem mem_essImage_of_unit_isSplitMono [Reflective i] {A : C}
   exact mem_ess_image_of_unit_is_iso A
 #align category_theory.mem_ess_image_of_unit_is_split_mono CategoryTheory.mem_essImage_of_unit_isSplitMono
 
+#print CategoryTheory.Reflective.comp /-
 /-- Composition of reflective functors. -/
 instance Reflective.comp (F : C ⥤ D) (G : D ⥤ E) [Fr : Reflective F] [Gr : Reflective G] :
     Reflective (F ⋙ G) where to_faithful := Faithful.comp F G
 #align category_theory.reflective.comp CategoryTheory.Reflective.comp
+-/
 
+/- warning: category_theory.unit_comp_partial_bijective_aux -> CategoryTheory.unitCompPartialBijectiveAux is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) (B : D), Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))
+but is expected to have type
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) (B : D), Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))
+Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_aux CategoryTheory.unitCompPartialBijectiveAuxₓ'. -/
 /-- (Implementation) Auxiliary definition for `unit_comp_partial_bijective`. -/
 def unitCompPartialBijectiveAux [Reflective i] (A : C) (B : D) :
     (A ⟶ i.obj B) ≃ (i.obj ((leftAdjoint i).obj A) ⟶ i.obj B) :=
   ((Adjunction.ofRightAdjoint i).homEquiv _ _).symm.trans (equivOfFullyFaithful i)
 #align category_theory.unit_comp_partial_bijective_aux CategoryTheory.unitCompPartialBijectiveAux
 
+/- warning: category_theory.unit_comp_partial_bijective_aux_symm_apply -> CategoryTheory.unitCompPartialBijectiveAux_symm_apply is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C} {B : D} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B))) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B)) (CategoryTheory.unitCompPartialBijectiveAux.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) A) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i B) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
+but is expected to have type
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] {A : C} {B : D} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B))) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B)) (CategoryTheory.unitCompPartialBijectiveAux.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) B) (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
+Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_aux_symm_apply CategoryTheory.unitCompPartialBijectiveAux_symm_applyₓ'. -/
 /-- The description of the inverse of the bijection `unit_comp_partial_bijective_aux`. -/
 theorem unitCompPartialBijectiveAux_symm_apply [Reflective i] {A : C} {B : D}
     (f : i.obj ((leftAdjoint i).obj A) ⟶ i.obj B) :
@@ -130,6 +176,12 @@ theorem unitCompPartialBijectiveAux_symm_apply [Reflective i] {A : C} {B : D}
   simp [unit_comp_partial_bijective_aux]
 #align category_theory.unit_comp_partial_bijective_aux_symm_apply CategoryTheory.unitCompPartialBijectiveAux_symm_apply
 
+/- warning: category_theory.unit_comp_partial_bijective -> CategoryTheory.unitCompPartialBijective is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C}, (Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) -> (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B))
+but is expected to have type
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C}, (Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) -> (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B))
+Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective CategoryTheory.unitCompPartialBijectiveₓ'. -/
 /-- If `i` has a reflector `L`, then the function `(i.obj (L.obj A) ⟶ B) → (A ⟶ B)` given by
 precomposing with `η.app A` is a bijection provided `B` is in the essential image of `i`.
 That is, the function `λ (f : i.obj (L.obj A) ⟶ B), η.app A ≫ f` is bijective, as long as `B` is in
@@ -150,24 +202,48 @@ def unitCompPartialBijective [Reflective i] (A : C) {B : C} (hB : B ∈ i.essIma
     
 #align category_theory.unit_comp_partial_bijective CategoryTheory.unitCompPartialBijective
 
+/- warning: category_theory.unit_comp_partial_bijective_symm_apply -> CategoryTheory.unitCompPartialBijective_symm_apply is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} (hB : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A (CategoryTheory.Functor.obj.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) A) B (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
+but is expected to have type
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) f) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1)) A) (Prefunctor.obj.{succ u1, succ u1, u3, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i)) A) B (CategoryTheory.NatTrans.app.{u1, u1, u3, u3} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u3} C _inst_1) (CategoryTheory.Functor.comp.{u1, u2, u1, u3, u4, u3} C _inst_1 D _inst_2 C _inst_1 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i) (CategoryTheory.Adjunction.unit.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) i (CategoryTheory.Adjunction.ofRightAdjoint.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A) f)
+Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_symm_apply CategoryTheory.unitCompPartialBijective_symm_applyₓ'. -/
 @[simp]
 theorem unitCompPartialBijective_symm_apply [Reflective i] (A : C) {B : C} (hB : B ∈ i.essImage)
     (f) : (unitCompPartialBijective A hB).symm f = (ofRightAdjoint i).Unit.app A ≫ f := by
   simp [unit_comp_partial_bijective, unit_comp_partial_bijective_aux_symm_apply]
 #align category_theory.unit_comp_partial_bijective_symm_apply CategoryTheory.unitCompPartialBijective_symm_apply
 
+/- warning: category_theory.unit_comp_partial_bijective_symm_natural -> CategoryTheory.unitCompPartialBijective_symm_natural is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB')) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) h)
+but is expected to have type
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' f h)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B')) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB')) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B)) (Equiv.symm.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB)) f) h)
+Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_symm_natural CategoryTheory.unitCompPartialBijective_symm_naturalₓ'. -/
 theorem unitCompPartialBijective_symm_natural [Reflective i] (A : C) {B B' : C} (h : B ⟶ B')
     (hB : B ∈ i.essImage) (hB' : B' ∈ i.essImage) (f : i.obj ((leftAdjoint i).obj A) ⟶ B) :
     (unitCompPartialBijective A hB').symm (f ≫ h) = (unitCompPartialBijective A hB).symm f ≫ h := by
   simp
 #align category_theory.unit_comp_partial_bijective_symm_natural CategoryTheory.unitCompPartialBijective_symm_natural
 
+/- warning: category_theory.unit_comp_partial_bijective_natural -> CategoryTheory.unitCompPartialBijective_natural is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B), Eq.{succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B') (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B')) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B B' (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) (fun (_x : Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) => (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) -> (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) (Equiv.hasCoeToFun.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 i (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4)) A)) B)) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB) f) h)
+but is expected to have type
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i] (A : C) {B : C} {B' : C} (h : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) B B') (hB : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (hB' : Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) B' (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B')) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B') _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B') (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B')) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B' hB') (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) A B B' f h)) (CategoryTheory.CategoryStruct.comp.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B B' (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B)) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (fun (_x : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) => Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) A B) (Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 (CategoryTheory.leftAdjoint.{u1, u2, u3, u4} C _inst_1 D _inst_2 i (CategoryTheory.Reflective.toIsRightAdjoint.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4))) A)) B)) (CategoryTheory.unitCompPartialBijective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i _inst_4 A B hB) f) h)
+Case conversion may be inaccurate. Consider using '#align category_theory.unit_comp_partial_bijective_natural CategoryTheory.unitCompPartialBijective_naturalₓ'. -/
 theorem unitCompPartialBijective_natural [Reflective i] (A : C) {B B' : C} (h : B ⟶ B')
     (hB : B ∈ i.essImage) (hB' : B' ∈ i.essImage) (f : A ⟶ B) :
     (unitCompPartialBijective A hB') (f ≫ h) = unitCompPartialBijective A hB f ≫ h := by
   rw [← Equiv.eq_symm_apply, unit_comp_partial_bijective_symm_natural A h, Equiv.symm_apply_apply]
 #align category_theory.unit_comp_partial_bijective_natural CategoryTheory.unitCompPartialBijective_natural
 
+/- warning: category_theory.equiv_ess_image_of_reflective -> CategoryTheory.equivEssImageOfReflective is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i], CategoryTheory.Equivalence.{u2, u1, u4, u3} D _inst_2 (CategoryTheory.Functor.EssImageSubcategory.{u2, u1, u4, u3} D C _inst_2 _inst_1 i) (CategoryTheory.Functor.EssImageSubcategory.category.{u1, u3, u4, u2} D C _inst_2 _inst_1 i)
+but is expected to have type
+  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {i : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1} [_inst_4 : CategoryTheory.Reflective.{u1, u2, u3, u4} C D _inst_1 _inst_2 i], CategoryTheory.Equivalence.{u2, u1, u4, u3} D (CategoryTheory.Functor.EssImageSubcategory.{u2, u1, u4, u3} D C _inst_2 _inst_1 i) _inst_2 (CategoryTheory.Functor.instCategoryEssImageSubcategory.{u2, u1, u4, u3} D C _inst_2 _inst_1 i)
+Case conversion may be inaccurate. Consider using '#align category_theory.equiv_ess_image_of_reflective CategoryTheory.equivEssImageOfReflectiveₓ'. -/
 /-- If `i : D ⥤ C` is reflective, the inverse functor of `i ≌ F.ess_image` can be explicitly
 defined by the reflector. -/
 @[simps]

239d882c

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

239d882c

chore: split CategoryTheory.MorphismProperty (#12393)

The file CategoryTheory.MorphismProperty is split into five files Basic, Composition, Limits, Concrete, IsInvertedBy.

9e489ab7

Diff

@@ -5,6 +5,7 @@ Authors: Bhavik Mehta
 -/
 import Mathlib.CategoryTheory.Adjunction.FullyFaithful
 import Mathlib.CategoryTheory.Conj
+import Mathlib.CategoryTheory.Functor.ReflectsIso
 
 #align_import category_theory.adjunction.reflective from "leanprover-community/mathlib"@"239d882c4fb58361ee8b3b39fb2091320edef10a"

239d882c

chore(CategoryTheory/Adjunction): move Adjunction.restrictFullyFaithful to separate file (#12363)

Also resolves a TODO to add lemmas about Adjunction.restrictFullyFaithful

38faa1d2

Diff

@@ -4,8 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 -/
 import Mathlib.CategoryTheory.Adjunction.FullyFaithful
-import Mathlib.CategoryTheory.Functor.ReflectsIso
-import Mathlib.CategoryTheory.EpiMono
+import Mathlib.CategoryTheory.Conj
 
 #align_import category_theory.adjunction.reflective from "leanprover-community/mathlib"@"239d882c4fb58361ee8b3b39fb2091320edef10a"

239d882c

chore(CategoryTheory/Adjunction): simplify some proofs in Adjunction/Reflective (#12375)

Some results in this file can be extracted from results added in #12344

81d26b1c

Diff

@@ -55,13 +55,8 @@ When restricted to objects in `D` given by `i : D ⥤ C`, the unit is an isomorp
 More generally this applies to objects essentially in the reflective subcategory, see
 `Functor.essImage.unit_isIso`.
 -/
-instance isIso_unit_obj [Reflective i] {B : D} : IsIso ((ofRightAdjoint i).unit.app (i.obj B)) := by
-  have : (ofRightAdjoint i).unit.app (i.obj B) = inv (i.map ((ofRightAdjoint i).counit.app B)) := by
-    rw [← comp_hom_eq_id]
-    apply (ofRightAdjoint i).right_triangle_components
-  rw [this]
-  exact IsIso.inv_isIso
-#align category_theory.is_iso_unit_obj CategoryTheory.isIso_unit_obj
+example [Reflective i] {B : D} : IsIso ((ofRightAdjoint i).unit.app (i.obj B)) :=
+  inferInstance
 
 /-- If `A` is essentially in the image of a reflective functor `i`, then `η_A` is an isomorphism.
 This gives that the "witness" for `A` being in the essential image can instead be given as the
@@ -71,13 +66,7 @@ reflection of `A`, with the isomorphism as `η_A`.
 -/
 theorem Functor.essImage.unit_isIso [Reflective i] {A : C} (h : A ∈ i.essImage) :
     IsIso ((ofRightAdjoint i).unit.app A) := by
-  suffices (ofRightAdjoint i).unit.app A = h.getIso.inv ≫
-      (ofRightAdjoint i).unit.app (i.obj (Functor.essImage.witness h)) ≫
-      (leftAdjoint i ⋙ i).map h.getIso.hom by
-    rw [this]
-    infer_instance
-  rw [← NatTrans.naturality]
-  simp
+  rwa [isIso_unit_app_iff_mem_essImage]
 #align category_theory.functor.ess_image.unit_is_iso CategoryTheory.Functor.essImage.unit_isIso
 
 /-- If `η_A` is an isomorphism, then `A` is in the essential image of `i`. -/

239d882c

chore: replace refine' that already have a ?_ (#12261)

Co-authored-by: Moritz Firsching <firsching@google.com>

94b44d32

Diff

@@ -166,7 +166,7 @@ Functor.essImage.unit_isIso X.property
 by `equivEssImageOfReflective` when the functor `i` is reflective. -/
 def equivEssImageOfReflective_counitIso_app [Reflective i] (X : Functor.EssImageSubcategory i) :
     ((Functor.essImageInclusion i ⋙ leftAdjoint i) ⋙ Functor.toEssImage i).obj X ≅ X := by
-  refine' Iso.symm (@asIso _ _ X _ ((ofRightAdjoint i).unit.app X.obj) ?_)
+  refine Iso.symm (@asIso _ _ X _ ((ofRightAdjoint i).unit.app X.obj) ?_)
   refine @isIso_of_reflects_iso _ _ _ _ _ _ _ i.essImageInclusion ?_ _
   dsimp
   exact inferInstance

239d882c

chore(CategoryTheory): move Full, Faithful, EssSurj, IsEquivalence and ReflectsIsomorphisms to the Functor namespace (#11985)

These notions on functors are now Functor.Full, Functor.Faithful, Functor.EssSurj, Functor.IsEquivalence, Functor.ReflectsIsomorphisms. Deprecated aliases are introduced for the previous names.

65b7affc

Diff

@@ -33,7 +33,7 @@ variable [Category.{v₁} C] [Category.{v₂} D] [Category.{v₃} E]
 /--
 A functor is *reflective*, or *a reflective inclusion*, if it is fully faithful and right adjoint.
 -/
-class Reflective (R : D ⥤ C) extends IsRightAdjoint R, Full R, Faithful R
+class Reflective (R : D ⥤ C) extends IsRightAdjoint R, R.Full, R.Faithful
 #align category_theory.reflective CategoryTheory.Reflective
 
 variable {i : D ⥤ C}
@@ -102,7 +102,7 @@ theorem mem_essImage_of_unit_isSplitMono [Reflective i] {A : C}
 
 /-- Composition of reflective functors. -/
 instance Reflective.comp (F : C ⥤ D) (G : D ⥤ E) [Reflective F] [Reflective G] :
-    Reflective (F ⋙ G) where toFaithful := Faithful.comp F G
+    Reflective (F ⋙ G) where
 #align category_theory.reflective.comp CategoryTheory.Reflective.comp
 
 /-- (Implementation) Auxiliary definition for `unitCompPartialBijective`. -/

239d882c

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -28,7 +28,6 @@ namespace CategoryTheory
 open Category Adjunction
 
 variable {C : Type u₁} {D : Type u₂} {E : Type u₃}
-
 variable [Category.{v₁} C] [Category.{v₂} D] [Category.{v₃} E]
 
 /--

239d882c

chore: remove useless tactics (#11333)

The removal of some pointless tactics flagged by #11308.

ee18bf38

Diff

@@ -97,7 +97,6 @@ theorem mem_essImage_of_unit_isSplitMono [Reflective i] {A : C}
     refine @epi_of_epi _ _ _ _ _ (retraction (η.app A)) (η.app A) ?_
     rw [show retraction _ ≫ η.app A = _ from η.naturality (retraction (η.app A))]
     apply epi_comp (η.app (i.obj ((leftAdjoint i).obj A)))
-  skip
   haveI := isIso_of_epi_of_isSplitMono (η.app A)
   exact mem_essImage_of_unit_isIso A
 #align category_theory.mem_ess_image_of_unit_is_split_mono CategoryTheory.mem_essImage_of_unit_isSplitMono

239d882c

chore: squeeze some non-terminal simps (#11247)

This PR accompanies #11246, squeezing some non-terminal simps highlighted by the linter until I decided to stop!

1ad8c3fe

Diff

@@ -177,7 +177,9 @@ lemma equivEssImageOfReflective_map_counitIso_app_hom [Reflective i]
     (X : Functor.EssImageSubcategory i) :
   (Functor.essImageInclusion i).map (equivEssImageOfReflective_counitIso_app X).hom =
     inv (NatTrans.app (ofRightAdjoint i).unit X.obj) := by
-    simp [equivEssImageOfReflective_counitIso_app, asIso]
+    simp only [Functor.comp_obj, Functor.essImageInclusion_obj, Functor.toEssImage_obj_obj,
+      equivEssImageOfReflective_counitIso_app, asIso, Iso.symm_mk, Functor.essImageInclusion_map,
+      Functor.id_obj]
     rfl
 
 lemma equivEssImageOfReflective_map_counitIso_app_inv [Reflective i]

239d882c

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -162,7 +162,7 @@ instance [Reflective i] (X : Functor.EssImageSubcategory i) :
   IsIso (NatTrans.app (ofRightAdjoint i).unit X.obj) :=
 Functor.essImage.unit_isIso X.property
 
--- porting note: the following auxiliary definition and the next two lemmas were
+-- Porting note: the following auxiliary definition and the next two lemmas were
 -- introduced in order to ease the port
 /-- The counit isomorphism of the equivalence `D ≌ i.EssImageSubcategory` given
 by `equivEssImageOfReflective` when the functor `i` is reflective. -/
@@ -211,7 +211,7 @@ def equivEssImageOfReflective [Reflective i] : D ≌ i.EssImageSubcategory
           equivEssImageOfReflective_map_counitIso_app_hom,
           IsIso.comp_inv_eq, assoc, ← h, IsIso.inv_hom_id_assoc, Functor.comp_map])
   functor_unitIso_comp := fun X => by
-    -- porting note: this proof was automatically handled by the automation in mathlib
+    -- Porting note: this proof was automatically handled by the automation in mathlib
     apply (Functor.essImageInclusion i).map_injective
     erw [Functor.map_comp, equivEssImageOfReflective_map_counitIso_app_hom]
     aesop_cat

239d882c

chore: replace Lean 3 syntax λ x, in doc comments (#10727)

Use Lean 4 syntax fun x ↦ instead, matching the style guide. This is close to exhaustive for doc comments; mathlib has about 460 remaining uses of λ (not all in Lean 3 syntax).

4a99b7e2

Diff

@@ -122,8 +122,8 @@ theorem unitCompPartialBijectiveAux_symm_apply [Reflective i] {A : C} {B : D}
 
 /-- If `i` has a reflector `L`, then the function `(i.obj (L.obj A) ⟶ B) → (A ⟶ B)` given by
 precomposing with `η.app A` is a bijection provided `B` is in the essential image of `i`.
-That is, the function `λ (f : i.obj (L.obj A) ⟶ B), η.app A ≫ f` is bijective, as long as `B` is in
-the essential image of `i`.
+That is, the function `fun (f : i.obj (L.obj A) ⟶ B) ↦ η.app A ≫ f` is bijective,
+as long as `B` is in the essential image of `i`.
 This definition gives an equivalence: the key property that the inverse can be described
 nicely is shown in `unitCompPartialBijective_symm_apply`.

239d882c

chore: exactly 4 spaces in subsequent lines for def (#7321)

Co-authored-by: Moritz Firsching <firsching@google.com>

11dbfb2b

Diff

@@ -167,21 +167,21 @@ Functor.essImage.unit_isIso X.property
 /-- The counit isomorphism of the equivalence `D ≌ i.EssImageSubcategory` given
 by `equivEssImageOfReflective` when the functor `i` is reflective. -/
 def equivEssImageOfReflective_counitIso_app [Reflective i] (X : Functor.EssImageSubcategory i) :
-  ((Functor.essImageInclusion i ⋙ leftAdjoint i) ⋙ Functor.toEssImage i).obj X ≅ X := by
+    ((Functor.essImageInclusion i ⋙ leftAdjoint i) ⋙ Functor.toEssImage i).obj X ≅ X := by
   refine' Iso.symm (@asIso _ _ X _ ((ofRightAdjoint i).unit.app X.obj) ?_)
   refine @isIso_of_reflects_iso _ _ _ _ _ _ _ i.essImageInclusion ?_ _
   dsimp
   exact inferInstance
 
 lemma equivEssImageOfReflective_map_counitIso_app_hom [Reflective i]
-  (X : Functor.EssImageSubcategory i) :
+    (X : Functor.EssImageSubcategory i) :
   (Functor.essImageInclusion i).map (equivEssImageOfReflective_counitIso_app X).hom =
     inv (NatTrans.app (ofRightAdjoint i).unit X.obj) := by
     simp [equivEssImageOfReflective_counitIso_app, asIso]
     rfl
 
 lemma equivEssImageOfReflective_map_counitIso_app_inv [Reflective i]
-  (X : Functor.EssImageSubcategory i) :
+    (X : Functor.EssImageSubcategory i) :
   (Functor.essImageInclusion i).map (equivEssImageOfReflective_counitIso_app X).inv =
     (NatTrans.app (ofRightAdjoint i).unit X.obj) := rfl

239d882c

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.adjunction.reflective
-! leanprover-community/mathlib commit 239d882c4fb58361ee8b3b39fb2091320edef10a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Adjunction.FullyFaithful
 import Mathlib.CategoryTheory.Functor.ReflectsIso
 import Mathlib.CategoryTheory.EpiMono
 
+#align_import category_theory.adjunction.reflective from "leanprover-community/mathlib"@"239d882c4fb58361ee8b3b39fb2091320edef10a"
+
 /-!
 # Reflective functors

239d882c

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -60,9 +60,7 @@ More generally this applies to objects essentially in the reflective subcategory
 `Functor.essImage.unit_isIso`.
 -/
 instance isIso_unit_obj [Reflective i] {B : D} : IsIso ((ofRightAdjoint i).unit.app (i.obj B)) := by
-  have :
-    (ofRightAdjoint i).unit.app (i.obj B) = inv (i.map ((ofRightAdjoint i).counit.app B)) :=
-    by
+  have : (ofRightAdjoint i).unit.app (i.obj B) = inv (i.map ((ofRightAdjoint i).counit.app B)) := by
     rw [← comp_hom_eq_id]
     apply (ofRightAdjoint i).right_triangle_components
   rw [this]
@@ -77,12 +75,9 @@ reflection of `A`, with the isomorphism as `η_A`.
 -/
 theorem Functor.essImage.unit_isIso [Reflective i] {A : C} (h : A ∈ i.essImage) :
     IsIso ((ofRightAdjoint i).unit.app A) := by
-  suffices
-    (ofRightAdjoint i).unit.app A =
-      h.getIso.inv ≫
-        (ofRightAdjoint i).unit.app (i.obj (Functor.essImage.witness h)) ≫
-          (leftAdjoint i ⋙ i).map h.getIso.hom
-    by
+  suffices (ofRightAdjoint i).unit.app A = h.getIso.inv ≫
+      (ofRightAdjoint i).unit.app (i.obj (Functor.essImage.witness h)) ≫
+      (leftAdjoint i ⋙ i).map h.getIso.hom by
     rw [this]
     infer_instance
   rw [← NatTrans.naturality]

239d882c

feat: port CategoryTheory.Adjunction.Reflective (#2467)

ffc42486

`category_theory.adjunction.reflective` ⟷ `Mathlib.CategoryTheory.Adjunction.Reflective`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 88

category_theory.adjunction.reflective ⟷ Mathlib.CategoryTheory.Adjunction.Reflective

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 88

`category_theory.adjunction.reflective` ⟷ `Mathlib.CategoryTheory.Adjunction.Reflective`