category_theory.limits.is_limit ⟷ Mathlib.CategoryTheory.Limits.IsLimit

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

@@ -515,9 +515,10 @@ def homIso' (h : IsLimit t) (W : C) :
 /-- If G : C → D is a faithful functor which sends t to a limit cone,
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/
-def ofFaithful {t : Cone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [Faithful G]
-    (ht : IsLimit (G.mapCone t)) (lift : ∀ s : Cone F, s.pt ⟶ t.pt)
-    (h : ∀ s, G.map (lift s) = ht.lift (G.mapCone s)) : IsLimit t :=
+def ofFaithful {t : Cone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D)
+    [CategoryTheory.Functor.Faithful G] (ht : IsLimit (G.mapCone t))
+    (lift : ∀ s : Cone F, s.pt ⟶ t.pt) (h : ∀ s, G.map (lift s) = ht.lift (G.mapCone s)) :
+    IsLimit t :=
   { lift
     fac := fun s j => by apply G.map_injective <;> rw [G.map_comp, h] <;> apply ht.fac
     uniq := fun s m w => by
@@ -1133,9 +1134,10 @@ def homIso' (h : IsColimit t) (W : C) :
 /-- If G : C → D is a faithful functor which sends t to a colimit cocone,
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/
-def ofFaithful {t : Cocone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [Faithful G]
-    (ht : IsColimit (G.mapCocone t)) (desc : ∀ s : Cocone F, t.pt ⟶ s.pt)
-    (h : ∀ s, G.map (desc s) = ht.desc (G.mapCocone s)) : IsColimit t :=
+def ofFaithful {t : Cocone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D)
+    [CategoryTheory.Functor.Faithful G] (ht : IsColimit (G.mapCocone t))
+    (desc : ∀ s : Cocone F, t.pt ⟶ s.pt) (h : ∀ s, G.map (desc s) = ht.desc (G.mapCocone s)) :
+    IsColimit t :=
   { desc
     fac := fun s j => by apply G.map_injective <;> rw [G.map_comp, h] <;> apply ht.fac
     uniq := fun s m w => by

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

@@ -608,8 +608,8 @@ theorem coneOfHom_fac {Y : C} (f : Y ⟶ X) : coneOfHom h f = (limitCone h).exte
   dsimp [cone_of_hom, limit_cone, cone.extend]
   congr with j
   have t := congr_fun (h.hom.naturality f.op) ⟨𝟙 X⟩
-  dsimp at t 
-  simp only [comp_id] at t 
+  dsimp at t
+  simp only [comp_id] at t
   rw [congr_fun (congr_arg nat_trans.app t) j]
   rfl
 #align category_theory.limits.is_limit.of_nat_iso.cone_of_hom_fac CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_fac
@@ -643,7 +643,7 @@ def ofNatIso {X : C} (h : yoneda.obj X ⋙ uliftFunctor.{u₁} ≅ F.cones) : Is
     have h := cone_fac h s
     cases s
     injection h with h₁ h₂
-    simp only [heq_iff_eq] at h₂ 
+    simp only [heq_iff_eq] at h₂
     conv_rhs => rw [← h₂]; rfl
   uniq s m w := by
     rw [← hom_of_cone_of_hom h m]
@@ -1227,8 +1227,8 @@ theorem coconeOfHom_fac {Y : C} (f : X ⟶ Y) : coconeOfHom h f = (colimitCocone
   dsimp [cocone_of_hom, colimit_cocone, cocone.extend]
   congr with j
   have t := congr_fun (h.hom.naturality f) ⟨𝟙 X⟩
-  dsimp at t 
-  simp only [id_comp] at t 
+  dsimp at t
+  simp only [id_comp] at t
   rw [congr_fun (congr_arg nat_trans.app t) j]
   rfl
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_fac CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_fac
@@ -1262,7 +1262,7 @@ def ofNatIso {X : C} (h : coyoneda.obj (op X) ⋙ uliftFunctor.{u₁} ≅ F.coco
     have h := cocone_fac h s
     cases s
     injection h with h₁ h₂
-    simp only [heq_iff_eq] at h₂ 
+    simp only [heq_iff_eq] at h₂
     conv_rhs => rw [← h₂]; rfl
   uniq s m w := by
     rw [← hom_of_cocone_of_hom h m]

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

@@ -3,8 +3,8 @@ Copyright (c) 2018 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Mario Carneiro, Scott Morrison, Floris van Doorn
 -/
-import Mathbin.CategoryTheory.Adjunction.Basic
-import Mathbin.CategoryTheory.Limits.Cones
+import CategoryTheory.Adjunction.Basic
+import CategoryTheory.Limits.Cones
 
 #align_import category_theory.limits.is_limit from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

@@ -66,12 +66,8 @@ structure IsLimit (t : Cone F) where
 #align category_theory.limits.is_limit CategoryTheory.Limits.IsLimit
 -/
 
-restate_axiom is_limit.fac'
-
 attribute [simp, reassoc] is_limit.fac
 
-restate_axiom is_limit.uniq'
-
 namespace IsLimit
 
 #print CategoryTheory.Limits.IsLimit.subsingleton /-
@@ -677,12 +673,8 @@ structure IsColimit (t : Cocone F) where
 #align category_theory.limits.is_colimit CategoryTheory.Limits.IsColimit
 -/
 
-restate_axiom is_colimit.fac'
-
 attribute [simp, reassoc] is_colimit.fac
 
-restate_axiom is_colimit.uniq'
-
 namespace IsColimit
 
 #print CategoryTheory.Limits.IsColimit.subsingleton /-

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

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Mario Carneiro, Scott Morrison, Floris van Doorn
-
-! This file was ported from Lean 3 source module category_theory.limits.is_limit
-! 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.Basic
 import Mathbin.CategoryTheory.Limits.Cones
 
+#align_import category_theory.limits.is_limit from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
+
 /-!
 # Limits and colimits
 

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

@@ -91,11 +91,13 @@ def map {F G : J ⥤ C} (s : Cone F) {t : Cone G} (P : IsLimit t) (α : F ⟶ G)
 #align category_theory.limits.is_limit.map CategoryTheory.Limits.IsLimit.map
 -/
 
+#print CategoryTheory.Limits.IsLimit.map_π /-
 @[simp, reassoc]
 theorem map_π {F G : J ⥤ C} (c : Cone F) {d : Cone G} (hd : IsLimit d) (α : F ⟶ G) (j : J) :
     hd.map c α ≫ d.π.app j = c.π.app j ≫ α.app j :=
   fac _ _ _
 #align category_theory.limits.is_limit.map_π CategoryTheory.Limits.IsLimit.map_π
+-/
 
 #print CategoryTheory.Limits.IsLimit.lift_self /-
 theorem lift_self {c : Cone F} (t : IsLimit c) : t.lift c = 𝟙 c.pt :=
@@ -118,17 +120,21 @@ theorem uniq_cone_morphism {s t : Cone F} (h : IsLimit t) {f f' : s ⟶ t} : f =
 #align category_theory.limits.is_limit.uniq_cone_morphism CategoryTheory.Limits.IsLimit.uniq_cone_morphism
 -/
 
+#print CategoryTheory.Limits.IsLimit.existsUnique /-
 /-- Restating the definition of a limit cone in terms of the ∃! operator. -/
 theorem existsUnique {t : Cone F} (h : IsLimit t) (s : Cone F) :
     ∃! l : s.pt ⟶ t.pt, ∀ j, l ≫ t.π.app j = s.π.app j :=
   ⟨h.lift s, h.fac s, h.uniq s⟩
 #align category_theory.limits.is_limit.exists_unique CategoryTheory.Limits.IsLimit.existsUnique
+-/
 
+#print CategoryTheory.Limits.IsLimit.ofExistsUnique /-
 /-- Noncomputably make a colimit cocone from the existence of unique factorizations. -/
 def ofExistsUnique {t : Cone F}
     (ht : ∀ s : Cone F, ∃! l : s.pt ⟶ t.pt, ∀ j, l ≫ t.π.app j = s.π.app j) : IsLimit t := by
   choose s hs hs' using ht; exact ⟨s, hs, hs'⟩
 #align category_theory.limits.is_limit.of_exists_unique CategoryTheory.Limits.IsLimit.ofExistsUnique
+-/
 
 #print CategoryTheory.Limits.IsLimit.mkConeMorphism /-
 /-- Alternative constructor for `is_limit`,
@@ -172,17 +178,21 @@ def conePointUniqueUpToIso {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) : s.pt
 #align category_theory.limits.is_limit.cone_point_unique_up_to_iso CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso
 -/
 
+#print CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp /-
 @[simp, reassoc]
 theorem conePointUniqueUpToIso_hom_comp {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) (j : J) :
     (conePointUniqueUpToIso P Q).Hom ≫ t.π.app j = s.π.app j :=
   (uniqueUpToIso P Q).Hom.w _
 #align category_theory.limits.is_limit.cone_point_unique_up_to_iso_hom_comp CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp
+-/
 
+#print CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp /-
 @[simp, reassoc]
 theorem conePointUniqueUpToIso_inv_comp {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) (j : J) :
     (conePointUniqueUpToIso P Q).inv ≫ s.π.app j = t.π.app j :=
   (uniqueUpToIso P Q).inv.w _
 #align category_theory.limits.is_limit.cone_point_unique_up_to_iso_inv_comp CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp
+-/
 
 #print CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_hom /-
 @[simp, reassoc]
@@ -259,6 +269,7 @@ def ofPointIso {r t : Cone F} (P : IsLimit r) [i : IsIso (P.lift t)] : IsLimit t
 
 variable {t : Cone F}
 
+#print CategoryTheory.Limits.IsLimit.hom_lift /-
 theorem hom_lift (h : IsLimit t) {W : C} (m : W ⟶ t.pt) :
     m =
       h.lift
@@ -268,14 +279,18 @@ theorem hom_lift (h : IsLimit t) {W : C} (m : W ⟶ t.pt) :
     { pt := W
       π := { app := fun b => m ≫ t.π.app b } } m fun b => rfl
 #align category_theory.limits.is_limit.hom_lift CategoryTheory.Limits.IsLimit.hom_lift
+-/
 
+#print CategoryTheory.Limits.IsLimit.hom_ext /-
 /-- Two morphisms into a limit are equal if their compositions with
   each cone morphism are equal. -/
 theorem hom_ext (h : IsLimit t) {W : C} {f f' : W ⟶ t.pt}
     (w : ∀ j, f ≫ t.π.app j = f' ≫ t.π.app j) : f = f' := by
   rw [h.hom_lift f, h.hom_lift f'] <;> congr <;> exact funext w
 #align category_theory.limits.is_limit.hom_ext CategoryTheory.Limits.IsLimit.hom_ext
+-/
 
+#print CategoryTheory.Limits.IsLimit.ofRightAdjoint /-
 /-- Given a right adjoint functor between categories of cones,
 the image of a limit cone is a limit cone.
 -/
@@ -284,7 +299,9 @@ def ofRightAdjoint {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G
   mkConeMorphism (fun s => (Adjunction.ofRightAdjoint h).homEquiv s c (t.liftConeMorphism _))
     fun s m => (Adjunction.eq_homEquiv_apply _ _ _).2 t.uniq_cone_morphism
 #align category_theory.limits.is_limit.of_right_adjoint CategoryTheory.Limits.IsLimit.ofRightAdjoint
+-/
 
+#print CategoryTheory.Limits.IsLimit.ofConeEquiv /-
 /-- Given two functors which have equivalent categories of cones, we can transport a limiting cone
 across the equivalence.
 -/
@@ -296,7 +313,9 @@ def ofConeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G 
   left_inv := by tidy
   right_inv := by tidy
 #align category_theory.limits.is_limit.of_cone_equiv CategoryTheory.Limits.IsLimit.ofConeEquiv
+-/
 
+#print CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc /-
 @[simp]
 theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G ≌ Cone F)
     {c : Cone G} (P : IsLimit (h.Functor.obj c)) (s) :
@@ -305,7 +324,9 @@ theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
         (h.unitIso.inv.app c).Hom :=
   rfl
 #align category_theory.limits.is_limit.of_cone_equiv_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc
+-/
 
+#print CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc /-
 @[simp]
 theorem ofConeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
     (h : Cone G ≌ Cone F) {c : Cone G} (P : IsLimit c) (s) :
@@ -313,7 +334,9 @@ theorem ofConeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K 
       (h.counitIso.inv.app s).Hom ≫ (h.Functor.map (P.liftConeMorphism (h.inverse.obj s))).Hom :=
   rfl
 #align category_theory.limits.is_limit.of_cone_equiv_symm_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc
+-/
 
+#print CategoryTheory.Limits.IsLimit.postcomposeHomEquiv /-
 /--
 A cone postcomposed with a natural isomorphism is a limit cone if and only if the original cone is.
 -/
@@ -321,7 +344,9 @@ def postcomposeHomEquiv {F G : J ⥤ C} (α : F ≅ G) (c : Cone F) :
     IsLimit ((Cones.postcompose α.Hom).obj c) ≃ IsLimit c :=
   ofConeEquiv (Cones.postcomposeEquivalence α)
 #align category_theory.limits.is_limit.postcompose_hom_equiv CategoryTheory.Limits.IsLimit.postcomposeHomEquiv
+-/
 
+#print CategoryTheory.Limits.IsLimit.postcomposeInvEquiv /-
 /-- A cone postcomposed with the inverse of a natural isomorphism is a limit cone if and only if
 the original cone is.
 -/
@@ -329,7 +354,9 @@ def postcomposeInvEquiv {F G : J ⥤ C} (α : F ≅ G) (c : Cone G) :
     IsLimit ((Cones.postcompose α.inv).obj c) ≃ IsLimit c :=
   postcomposeHomEquiv α.symm c
 #align category_theory.limits.is_limit.postcompose_inv_equiv CategoryTheory.Limits.IsLimit.postcomposeInvEquiv
+-/
 
+#print CategoryTheory.Limits.IsLimit.equivOfNatIsoOfIso /-
 /-- Constructing an equivalence `is_limit c ≃ is_limit d` from a natural isomorphism
 between the underlying functors, and then an isomorphism between `c` transported along this and `d`.
 -/
@@ -337,6 +364,7 @@ def equivOfNatIsoOfIso {F G : J ⥤ C} (α : F ≅ G) (c : Cone F) (d : Cone G)
     (w : (Cones.postcompose α.Hom).obj c ≅ d) : IsLimit c ≃ IsLimit d :=
   (postcomposeHomEquiv α _).symm.trans (equivIsoLimit w)
 #align category_theory.limits.is_limit.equiv_of_nat_iso_of_iso CategoryTheory.Limits.IsLimit.equivOfNatIsoOfIso
+-/
 
 #print CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso /-
 /-- The cone points of two limit cones for naturally isomorphic functors
@@ -352,17 +380,21 @@ def conePointsIsoOfNatIso {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit
 #align category_theory.limits.is_limit.cone_points_iso_of_nat_iso CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso
 -/
 
+#print CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp /-
 @[reassoc]
 theorem conePointsIsoOfNatIso_hom_comp {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit s)
     (Q : IsLimit t) (w : F ≅ G) (j : J) :
     (conePointsIsoOfNatIso P Q w).Hom ≫ t.π.app j = s.π.app j ≫ w.Hom.app j := by simp
 #align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_hom_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp
+-/
 
+#print CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp /-
 @[reassoc]
 theorem conePointsIsoOfNatIso_inv_comp {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit s)
     (Q : IsLimit t) (w : F ≅ G) (j : J) :
     (conePointsIsoOfNatIso P Q w).inv ≫ s.π.app j = t.π.app j ≫ w.inv.app j := by simp
 #align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_inv_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp
+-/
 
 #print CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom /-
 @[reassoc]
@@ -386,25 +418,32 @@ section Equivalence
 
 open CategoryTheory.Equivalence
 
+#print CategoryTheory.Limits.IsLimit.whiskerEquivalence /-
 /-- If `s : cone F` is a limit cone, so is `s` whiskered by an equivalence `e`.
 -/
 def whiskerEquivalence {s : Cone F} (P : IsLimit s) (e : K ≌ J) : IsLimit (s.whisker e.Functor) :=
   ofRightAdjoint (Cones.whiskeringEquivalence e).Functor P
 #align category_theory.limits.is_limit.whisker_equivalence CategoryTheory.Limits.IsLimit.whiskerEquivalence
+-/
 
+#print CategoryTheory.Limits.IsLimit.ofWhiskerEquivalence /-
 /-- If `s : cone F` whiskered by an equivalence `e` is a limit cone, so is `s`.
 -/
 def ofWhiskerEquivalence {s : Cone F} (e : K ≌ J) (P : IsLimit (s.whisker e.Functor)) : IsLimit s :=
   equivIsoLimit ((Cones.whiskeringEquivalence e).unitIso.app s).symm
     (ofRightAdjoint (Cones.whiskeringEquivalence e).inverse P : _)
 #align category_theory.limits.is_limit.of_whisker_equivalence CategoryTheory.Limits.IsLimit.ofWhiskerEquivalence
+-/
 
+#print CategoryTheory.Limits.IsLimit.whiskerEquivalenceEquiv /-
 /-- Given an equivalence of diagrams `e`, `s` is a limit cone iff `s.whisker e.functor` is.
 -/
 def whiskerEquivalenceEquiv {s : Cone F} (e : K ≌ J) : IsLimit s ≃ IsLimit (s.whisker e.Functor) :=
   ⟨fun h => h.whiskerEquivalence e, ofWhiskerEquivalence e, by tidy, by tidy⟩
 #align category_theory.limits.is_limit.whisker_equivalence_equiv CategoryTheory.Limits.IsLimit.whiskerEquivalenceEquiv
+-/
 
+#print CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence /-
 /-- We can prove two cone points `(s : cone F).X` and `(t.cone G).X` are isomorphic if
 * both cones are limit cones
 * their indexing categories are equivalent via some `e : J ≌ K`,
@@ -429,9 +468,11 @@ def conePointsIsoOfEquivalence {F : J ⥤ C} {s : Cone F} {G : K ⥤ C} {t : Con
       simp
     inv_hom_id' := by apply hom_ext Q; tidy }
 #align category_theory.limits.is_limit.cone_points_iso_of_equivalence CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence
+-/
 
 end Equivalence
 
+#print CategoryTheory.Limits.IsLimit.homIso /-
 /-- The universal property of a limit cone: a map `W ⟶ X` is the same as
   a cone on `F` with vertex `W`. -/
 def homIso (h : IsLimit t) (W : C) : ULift.{u₁} (W ⟶ t.pt : Type v₃) ≅ (const J).obj W ⟶ F
@@ -443,19 +484,25 @@ def homIso (h : IsLimit t) (W : C) : ULift.{u₁} (W ⟶ t.pt : Type v₃) ≅ (
           π }⟩
   hom_inv_id' := by ext f <;> apply h.hom_ext <;> intro j <;> simp <;> dsimp <;> rfl
 #align category_theory.limits.is_limit.hom_iso CategoryTheory.Limits.IsLimit.homIso
+-/
 
+#print CategoryTheory.Limits.IsLimit.homIso_hom /-
 @[simp]
 theorem homIso_hom (h : IsLimit t) {W : C} (f : ULift.{u₁} (W ⟶ t.pt)) :
     (IsLimit.homIso h W).Hom f = (t.extend f.down).π :=
   rfl
 #align category_theory.limits.is_limit.hom_iso_hom CategoryTheory.Limits.IsLimit.homIso_hom
+-/
 
+#print CategoryTheory.Limits.IsLimit.natIso /-
 /-- The limit of `F` represents the functor taking `W` to
   the set of cones on `F` with vertex `W`. -/
 def natIso (h : IsLimit t) : yoneda.obj t.pt ⋙ uliftFunctor.{u₁} ≅ F.cones :=
   NatIso.ofComponents (fun W => IsLimit.homIso h (unop W)) (by tidy)
 #align category_theory.limits.is_limit.nat_iso CategoryTheory.Limits.IsLimit.natIso
+-/
 
+#print CategoryTheory.Limits.IsLimit.homIso' /-
 /-- Another, more explicit, formulation of the universal property of a limit cone.
 See also `hom_iso`.
 -/
@@ -469,7 +516,9 @@ def homIso' (h : IsLimit t) (W : C) :
         { app := fun j => p.1 j
           naturality' := fun j j' f => by dsimp; rw [id_comp]; exact (p.2 f).symm } }
 #align category_theory.limits.is_limit.hom_iso' CategoryTheory.Limits.IsLimit.homIso'
+-/
 
+#print CategoryTheory.Limits.IsLimit.ofFaithful /-
 /-- If G : C → D is a faithful functor which sends t to a limit cone,
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/
@@ -484,7 +533,9 @@ def ofFaithful {t : Cone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [F
       convert ← congr_arg (fun f => G.map f) (w j)
       apply G.map_comp }
 #align category_theory.limits.is_limit.of_faithful CategoryTheory.Limits.IsLimit.ofFaithful
+-/
 
+#print CategoryTheory.Limits.IsLimit.mapConeEquiv /-
 /-- If `F` and `G` are naturally isomorphic, then `F.map_cone c` being a limit implies
 `G.map_cone c` is also a limit.
 -/
@@ -494,6 +545,7 @@ def mapConeEquiv {D : Type u₄} [Category.{v₄} D] {K : J ⥤ C} {F G : C ⥤
   apply postcompose_inv_equiv (iso_whisker_left K h : _) (G.map_cone c) _
   apply t.of_iso_limit (postcompose_whisker_left_map_cone h.symm c).symm
 #align category_theory.limits.is_limit.map_cone_equiv CategoryTheory.Limits.IsLimit.mapConeEquiv
+-/
 
 #print CategoryTheory.Limits.IsLimit.isoUniqueConeMorphism /-
 /-- A cone is a limit cone exactly if
@@ -514,18 +566,23 @@ namespace OfNatIso
 
 variable {X : C} (h : yoneda.obj X ⋙ uliftFunctor.{u₁} ≅ F.cones)
 
+#print CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom /-
 /-- If `F.cones` is represented by `X`, each morphism `f : Y ⟶ X` gives a cone with cone point
 `Y`. -/
 def coneOfHom {Y : C} (f : Y ⟶ X) : Cone F where
   pt := Y
   π := h.Hom.app (op Y) ⟨f⟩
 #align category_theory.limits.is_limit.of_nat_iso.cone_of_hom CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom
+-/
 
+#print CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone /-
 /-- If `F.cones` is represented by `X`, each cone `s` gives a morphism `s.X ⟶ X`. -/
 def homOfCone (s : Cone F) : s.pt ⟶ X :=
   (h.inv.app (op s.pt) s.π).down
 #align category_theory.limits.is_limit.of_nat_iso.hom_of_cone CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone
+-/
 
+#print CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_homOfCone /-
 @[simp]
 theorem coneOfHom_homOfCone (s : Cone F) : coneOfHom h (homOfCone h s) = s :=
   by
@@ -533,18 +590,24 @@ theorem coneOfHom_homOfCone (s : Cone F) : coneOfHom h (homOfCone h s) = s :=
   convert congr_fun (congr_fun (congr_arg nat_trans.app h.inv_hom_id) (op s_X)) s_π
   exact ULift.up_down _
 #align category_theory.limits.is_limit.of_nat_iso.cone_of_hom_of_cone CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_homOfCone
+-/
 
+#print CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone_coneOfHom /-
 @[simp]
 theorem homOfCone_coneOfHom {Y : C} (f : Y ⟶ X) : homOfCone h (coneOfHom h f) = f :=
   congr_arg ULift.down (congr_fun (congr_fun (congr_arg NatTrans.app h.hom_inv_id) (op Y)) ⟨f⟩ : _)
 #align category_theory.limits.is_limit.of_nat_iso.hom_of_cone_of_hom CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone_coneOfHom
+-/
 
+#print CategoryTheory.Limits.IsLimit.OfNatIso.limitCone /-
 /-- If `F.cones` is represented by `X`, the cone corresponding to the identity morphism on `X`
 will be a limit cone. -/
 def limitCone : Cone F :=
   coneOfHom h (𝟙 X)
 #align category_theory.limits.is_limit.of_nat_iso.limit_cone CategoryTheory.Limits.IsLimit.OfNatIso.limitCone
+-/
 
+#print CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_fac /-
 /-- If `F.cones` is represented by `X`, the cone corresponding to a morphism `f : Y ⟶ X` is
 the limit cone extended by `f`. -/
 theorem coneOfHom_fac {Y : C} (f : Y ⟶ X) : coneOfHom h f = (limitCone h).extend f :=
@@ -557,7 +620,9 @@ theorem coneOfHom_fac {Y : C} (f : Y ⟶ X) : coneOfHom h f = (limitCone h).exte
   rw [congr_fun (congr_arg nat_trans.app t) j]
   rfl
 #align category_theory.limits.is_limit.of_nat_iso.cone_of_hom_fac CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_fac
+-/
 
+#print CategoryTheory.Limits.IsLimit.OfNatIso.cone_fac /-
 /-- If `F.cones` is represented by `X`, any cone is the extension of the limit cone by the
 corresponding morphism. -/
 theorem cone_fac (s : Cone F) : (limitCone h).extend (homOfCone h s) = s :=
@@ -566,6 +631,7 @@ theorem cone_fac (s : Cone F) : (limitCone h).extend (homOfCone h s) = s :=
   conv_lhs => simp only [hom_of_cone_of_hom]
   apply (cone_of_hom_fac _ _).symm
 #align category_theory.limits.is_limit.of_nat_iso.cone_fac CategoryTheory.Limits.IsLimit.OfNatIso.cone_fac
+-/
 
 end OfNatIso
 
@@ -573,6 +639,7 @@ section
 
 open OfNatIso
 
+#print CategoryTheory.Limits.IsLimit.ofNatIso /-
 /-- If `F.cones` is representable, then the cone corresponding to the identity morphism on
 the representing object is a limit cone.
 -/
@@ -591,6 +658,7 @@ def ofNatIso {X : C} (h : yoneda.obj X ⋙ uliftFunctor.{u₁} ≅ F.cones) : Is
     rw [cone_of_hom_fac]
     dsimp [cone.extend]; cases s; congr with j; exact w j
 #align category_theory.limits.is_limit.of_nat_iso CategoryTheory.Limits.IsLimit.ofNatIso
+-/
 
 end
 
@@ -634,11 +702,13 @@ def map {F G : J ⥤ C} {s : Cocone F} (P : IsColimit s) (t : Cocone G) (α : F
 #align category_theory.limits.is_colimit.map CategoryTheory.Limits.IsColimit.map
 -/
 
+#print CategoryTheory.Limits.IsColimit.ι_map /-
 @[simp, reassoc]
 theorem ι_map {F G : J ⥤ C} {c : Cocone F} (hc : IsColimit c) (d : Cocone G) (α : F ⟶ G) (j : J) :
     c.ι.app j ≫ IsColimit.map hc d α = α.app j ≫ d.ι.app j :=
   fac _ _ _
 #align category_theory.limits.is_colimit.ι_map CategoryTheory.Limits.IsColimit.ι_map
+-/
 
 #print CategoryTheory.Limits.IsColimit.desc_self /-
 @[simp]
@@ -662,17 +732,21 @@ theorem uniq_cocone_morphism {s t : Cocone F} (h : IsColimit t) {f f' : t ⟶ s}
 #align category_theory.limits.is_colimit.uniq_cocone_morphism CategoryTheory.Limits.IsColimit.uniq_cocone_morphism
 -/
 
+#print CategoryTheory.Limits.IsColimit.existsUnique /-
 /-- Restating the definition of a colimit cocone in terms of the ∃! operator. -/
 theorem existsUnique {t : Cocone F} (h : IsColimit t) (s : Cocone F) :
     ∃! d : t.pt ⟶ s.pt, ∀ j, t.ι.app j ≫ d = s.ι.app j :=
   ⟨h.desc s, h.fac s, h.uniq s⟩
 #align category_theory.limits.is_colimit.exists_unique CategoryTheory.Limits.IsColimit.existsUnique
+-/
 
+#print CategoryTheory.Limits.IsColimit.ofExistsUnique /-
 /-- Noncomputably make a colimit cocone from the existence of unique factorizations. -/
 def ofExistsUnique {t : Cocone F}
     (ht : ∀ s : Cocone F, ∃! d : t.pt ⟶ s.pt, ∀ j, t.ι.app j ≫ d = s.ι.app j) : IsColimit t := by
   choose s hs hs' using ht; exact ⟨s, hs, hs'⟩
 #align category_theory.limits.is_colimit.of_exists_unique CategoryTheory.Limits.IsColimit.ofExistsUnique
+-/
 
 #print CategoryTheory.Limits.IsColimit.mkCoconeMorphism /-
 /-- Alternative constructor for `is_colimit`,
@@ -716,17 +790,21 @@ def coconePointUniqueUpToIso {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t
 #align category_theory.limits.is_colimit.cocone_point_unique_up_to_iso CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso
 -/
 
+#print CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom /-
 @[simp, reassoc]
 theorem comp_coconePointUniqueUpToIso_hom {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t)
     (j : J) : s.ι.app j ≫ (coconePointUniqueUpToIso P Q).Hom = t.ι.app j :=
   (uniqueUpToIso P Q).Hom.w _
 #align category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_hom CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom
+-/
 
+#print CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv /-
 @[simp, reassoc]
 theorem comp_coconePointUniqueUpToIso_inv {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t)
     (j : J) : t.ι.app j ≫ (coconePointUniqueUpToIso P Q).inv = s.ι.app j :=
   (uniqueUpToIso P Q).inv.w _
 #align category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_inv CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv
+-/
 
 #print CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc /-
 @[simp, reassoc]
@@ -802,6 +880,7 @@ def ofPointIso {r t : Cocone F} (P : IsColimit r) [i : IsIso (P.desc t)] : IsCol
 
 variable {t : Cocone F}
 
+#print CategoryTheory.Limits.IsColimit.hom_desc /-
 theorem hom_desc (h : IsColimit t) {W : C} (m : t.pt ⟶ W) :
     m =
       h.desc
@@ -816,14 +895,18 @@ theorem hom_desc (h : IsColimit t) {W : C} (m : t.pt ⟶ W) :
           naturality' := _ } }
     m fun b => rfl
 #align category_theory.limits.is_colimit.hom_desc CategoryTheory.Limits.IsColimit.hom_desc
+-/
 
+#print CategoryTheory.Limits.IsColimit.hom_ext /-
 /-- Two morphisms out of a colimit are equal if their compositions with
   each cocone morphism are equal. -/
 theorem hom_ext (h : IsColimit t) {W : C} {f f' : t.pt ⟶ W}
     (w : ∀ j, t.ι.app j ≫ f = t.ι.app j ≫ f') : f = f' := by
   rw [h.hom_desc f, h.hom_desc f'] <;> congr <;> exact funext w
 #align category_theory.limits.is_colimit.hom_ext CategoryTheory.Limits.IsColimit.hom_ext
+-/
 
+#print CategoryTheory.Limits.IsColimit.ofLeftAdjoint /-
 /-- Given a left adjoint functor between categories of cocones,
 the image of a colimit cocone is a colimit cocone.
 -/
@@ -833,7 +916,9 @@ def ofLeftAdjoint {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cocone
     (fun s => ((Adjunction.ofLeftAdjoint h).homEquiv c s).symm (t.descCoconeMorphism _)) fun s m =>
     (Adjunction.homEquiv_apply_eq _ _ _).1 t.uniq_cocone_morphism
 #align category_theory.limits.is_colimit.of_left_adjoint CategoryTheory.Limits.IsColimit.ofLeftAdjoint
+-/
 
+#print CategoryTheory.Limits.IsColimit.ofCoconeEquiv /-
 /-- Given two functors which have equivalent categories of cocones,
 we can transport a colimiting cocone across the equivalence.
 -/
@@ -845,7 +930,9 @@ def ofCoconeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cocone
   left_inv := by tidy
   right_inv := by tidy
 #align category_theory.limits.is_colimit.of_cocone_equiv CategoryTheory.Limits.IsColimit.ofCoconeEquiv
+-/
 
+#print CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc /-
 @[simp]
 theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
     (h : Cocone G ≌ Cocone F) {c : Cocone G} (P : IsColimit (h.Functor.obj c)) (s) :
@@ -854,7 +941,9 @@ theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤
         (h.inverse.map (P.descCoconeMorphism (h.Functor.obj s))).Hom ≫ (h.unitInv.app s).Hom :=
   rfl
 #align category_theory.limits.is_colimit.of_cocone_equiv_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc
+-/
 
+#print CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc /-
 @[simp]
 theorem ofCoconeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
     (h : Cocone G ≌ Cocone F) {c : Cocone G} (P : IsColimit c) (s) :
@@ -862,7 +951,9 @@ theorem ofCoconeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K
       (h.Functor.map (P.descCoconeMorphism (h.inverse.obj s))).Hom ≫ (h.counit.app s).Hom :=
   rfl
 #align category_theory.limits.is_colimit.of_cocone_equiv_symm_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc
+-/
 
+#print CategoryTheory.Limits.IsColimit.precomposeHomEquiv /-
 /-- A cocone precomposed with a natural isomorphism is a colimit cocone
 if and only if the original cocone is.
 -/
@@ -870,7 +961,9 @@ def precomposeHomEquiv {F G : J ⥤ C} (α : F ≅ G) (c : Cocone G) :
     IsColimit ((Cocones.precompose α.Hom).obj c) ≃ IsColimit c :=
   ofCoconeEquiv (Cocones.precomposeEquivalence α)
 #align category_theory.limits.is_colimit.precompose_hom_equiv CategoryTheory.Limits.IsColimit.precomposeHomEquiv
+-/
 
+#print CategoryTheory.Limits.IsColimit.precomposeInvEquiv /-
 /-- A cocone precomposed with the inverse of a natural isomorphism is a colimit cocone
 if and only if the original cocone is.
 -/
@@ -878,7 +971,9 @@ def precomposeInvEquiv {F G : J ⥤ C} (α : F ≅ G) (c : Cocone F) :
     IsColimit ((Cocones.precompose α.inv).obj c) ≃ IsColimit c :=
   precomposeHomEquiv α.symm c
 #align category_theory.limits.is_colimit.precompose_inv_equiv CategoryTheory.Limits.IsColimit.precomposeInvEquiv
+-/
 
+#print CategoryTheory.Limits.IsColimit.equivOfNatIsoOfIso /-
 /-- Constructing an equivalence `is_colimit c ≃ is_colimit d` from a natural isomorphism
 between the underlying functors, and then an isomorphism between `c` transported along this and `d`.
 -/
@@ -886,6 +981,7 @@ def equivOfNatIsoOfIso {F G : J ⥤ C} (α : F ≅ G) (c : Cocone F) (d : Cocone
     (w : (Cocones.precompose α.inv).obj c ≅ d) : IsColimit c ≃ IsColimit d :=
   (precomposeInvEquiv α _).symm.trans (equivIsoColimit w)
 #align category_theory.limits.is_colimit.equiv_of_nat_iso_of_iso CategoryTheory.Limits.IsColimit.equivOfNatIsoOfIso
+-/
 
 #print CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso /-
 /-- The cocone points of two colimit cocones for naturally isomorphic functors
@@ -902,17 +998,21 @@ def coconePointsIsoOfNatIso {F G : J ⥤ C} {s : Cocone F} {t : Cocone G} (P : I
 #align category_theory.limits.is_colimit.cocone_points_iso_of_nat_iso CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso
 -/
 
+#print CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom /-
 @[reassoc]
 theorem comp_coconePointsIsoOfNatIso_hom {F G : J ⥤ C} {s : Cocone F} {t : Cocone G}
     (P : IsColimit s) (Q : IsColimit t) (w : F ≅ G) (j : J) :
     s.ι.app j ≫ (coconePointsIsoOfNatIso P Q w).Hom = w.Hom.app j ≫ t.ι.app j := by simp
 #align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_hom CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom
+-/
 
+#print CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv /-
 @[reassoc]
 theorem comp_coconePointsIsoOfNatIso_inv {F G : J ⥤ C} {s : Cocone F} {t : Cocone G}
     (P : IsColimit s) (Q : IsColimit t) (w : F ≅ G) (j : J) :
     t.ι.app j ≫ (coconePointsIsoOfNatIso P Q w).inv = w.inv.app j ≫ s.ι.app j := by simp
 #align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_inv CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv
+-/
 
 #print CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc /-
 @[reassoc]
@@ -936,13 +1036,16 @@ section Equivalence
 
 open CategoryTheory.Equivalence
 
+#print CategoryTheory.Limits.IsColimit.whiskerEquivalence /-
 /-- If `s : cocone F` is a colimit cocone, so is `s` whiskered by an equivalence `e`.
 -/
 def whiskerEquivalence {s : Cocone F} (P : IsColimit s) (e : K ≌ J) :
     IsColimit (s.whisker e.Functor) :=
   ofLeftAdjoint (Cocones.whiskeringEquivalence e).Functor P
 #align category_theory.limits.is_colimit.whisker_equivalence CategoryTheory.Limits.IsColimit.whiskerEquivalence
+-/
 
+#print CategoryTheory.Limits.IsColimit.ofWhiskerEquivalence /-
 /-- If `s : cocone F` whiskered by an equivalence `e` is a colimit cocone, so is `s`.
 -/
 def ofWhiskerEquivalence {s : Cocone F} (e : K ≌ J) (P : IsColimit (s.whisker e.Functor)) :
@@ -950,14 +1053,18 @@ def ofWhiskerEquivalence {s : Cocone F} (e : K ≌ J) (P : IsColimit (s.whisker
   equivIsoColimit ((Cocones.whiskeringEquivalence e).unitIso.app s).symm
     (ofLeftAdjoint (Cocones.whiskeringEquivalence e).inverse P : _)
 #align category_theory.limits.is_colimit.of_whisker_equivalence CategoryTheory.Limits.IsColimit.ofWhiskerEquivalence
+-/
 
+#print CategoryTheory.Limits.IsColimit.whiskerEquivalenceEquiv /-
 /-- Given an equivalence of diagrams `e`, `s` is a colimit cocone iff `s.whisker e.functor` is.
 -/
 def whiskerEquivalenceEquiv {s : Cocone F} (e : K ≌ J) :
     IsColimit s ≃ IsColimit (s.whisker e.Functor) :=
   ⟨fun h => h.whiskerEquivalence e, ofWhiskerEquivalence e, by tidy, by tidy⟩
 #align category_theory.limits.is_colimit.whisker_equivalence_equiv CategoryTheory.Limits.IsColimit.whiskerEquivalenceEquiv
+-/
 
+#print CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence /-
 /-- We can prove two cocone points `(s : cocone F).X` and `(t.cocone G).X` are isomorphic if
 * both cocones are colimit cocones
 * their indexing categories are equivalent via some `e : J ≌ K`,
@@ -983,9 +1090,11 @@ def coconePointsIsoOfEquivalence {F : J ⥤ C} {s : Cocone F} {G : K ⥤ C} {t :
       simp
     inv_hom_id' := by apply hom_ext Q; tidy }
 #align category_theory.limits.is_colimit.cocone_points_iso_of_equivalence CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence
+-/
 
 end Equivalence
 
+#print CategoryTheory.Limits.IsColimit.homIso /-
 /-- The universal property of a colimit cocone: a map `X ⟶ W` is the same as
   a cocone on `F` with vertex `W`. -/
 def homIso (h : IsColimit t) (W : C) : ULift.{u₁} (t.pt ⟶ W : Type v₃) ≅ F ⟶ (const J).obj W
@@ -997,19 +1106,25 @@ def homIso (h : IsColimit t) (W : C) : ULift.{u₁} (t.pt ⟶ W : Type v₃) ≅
           ι }⟩
   hom_inv_id' := by ext f <;> apply h.hom_ext <;> intro j <;> simp <;> dsimp <;> rfl
 #align category_theory.limits.is_colimit.hom_iso CategoryTheory.Limits.IsColimit.homIso
+-/
 
+#print CategoryTheory.Limits.IsColimit.homIso_hom /-
 @[simp]
 theorem homIso_hom (h : IsColimit t) {W : C} (f : ULift (t.pt ⟶ W)) :
     (IsColimit.homIso h W).Hom f = (t.extend f.down).ι :=
   rfl
 #align category_theory.limits.is_colimit.hom_iso_hom CategoryTheory.Limits.IsColimit.homIso_hom
+-/
 
+#print CategoryTheory.Limits.IsColimit.natIso /-
 /-- The colimit of `F` represents the functor taking `W` to
   the set of cocones on `F` with vertex `W`. -/
 def natIso (h : IsColimit t) : coyoneda.obj (op t.pt) ⋙ uliftFunctor.{u₁} ≅ F.cocones :=
   NatIso.ofComponents (IsColimit.homIso h) (by intros <;> ext <;> dsimp <;> rw [← assoc] <;> rfl)
 #align category_theory.limits.is_colimit.nat_iso CategoryTheory.Limits.IsColimit.natIso
+-/
 
+#print CategoryTheory.Limits.IsColimit.homIso' /-
 /-- Another, more explicit, formulation of the universal property of a colimit cocone.
 See also `hom_iso`.
 -/
@@ -1023,7 +1138,9 @@ def homIso' (h : IsColimit t) (W : C) :
         { app := fun j => p.1 j
           naturality' := fun j j' f => by dsimp; rw [comp_id]; exact p.2 f } }
 #align category_theory.limits.is_colimit.hom_iso' CategoryTheory.Limits.IsColimit.homIso'
+-/
 
+#print CategoryTheory.Limits.IsColimit.ofFaithful /-
 /-- If G : C → D is a faithful functor which sends t to a colimit cocone,
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/
@@ -1038,7 +1155,9 @@ def ofFaithful {t : Cocone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D)
       convert ← congr_arg (fun f => G.map f) (w j)
       apply G.map_comp }
 #align category_theory.limits.is_colimit.of_faithful CategoryTheory.Limits.IsColimit.ofFaithful
+-/
 
+#print CategoryTheory.Limits.IsColimit.mapCoconeEquiv /-
 /-- If `F` and `G` are naturally isomorphic, then `F.map_cone c` being a colimit implies
 `G.map_cone c` is also a colimit.
 -/
@@ -1048,6 +1167,7 @@ def mapCoconeEquiv {D : Type u₄} [Category.{v₄} D] {K : J ⥤ C} {F G : C 
   apply is_colimit.of_iso_colimit _ (precompose_whisker_left_map_cocone h c)
   apply (precompose_inv_equiv (iso_whisker_left K h : _) _).symm t
 #align category_theory.limits.is_colimit.map_cocone_equiv CategoryTheory.Limits.IsColimit.mapCoconeEquiv
+-/
 
 #print CategoryTheory.Limits.IsColimit.isoUniqueCoconeMorphism /-
 /-- A cocone is a colimit cocone exactly if
@@ -1068,6 +1188,7 @@ namespace OfNatIso
 
 variable {X : C} (h : coyoneda.obj (op X) ⋙ uliftFunctor.{u₁} ≅ F.cocones)
 
+#print CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom /-
 /-- If `F.cocones` is corepresented by `X`, each morphism `f : X ⟶ Y` gives a cocone with cone
 point `Y`. -/
 def coconeOfHom {Y : C} (f : X ⟶ Y) : Cocone F
@@ -1075,12 +1196,16 @@ def coconeOfHom {Y : C} (f : X ⟶ Y) : Cocone F
   pt := Y
   ι := h.Hom.app Y ⟨f⟩
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom
+-/
 
+#print CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone /-
 /-- If `F.cocones` is corepresented by `X`, each cocone `s` gives a morphism `X ⟶ s.X`. -/
 def homOfCocone (s : Cocone F) : X ⟶ s.pt :=
   (h.inv.app s.pt s.ι).down
 #align category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone
+-/
 
+#print CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_homOfCocone /-
 @[simp]
 theorem coconeOfHom_homOfCocone (s : Cocone F) : coconeOfHom h (homOfCocone h s) = s :=
   by
@@ -1088,18 +1213,24 @@ theorem coconeOfHom_homOfCocone (s : Cocone F) : coconeOfHom h (homOfCocone h s)
   convert congr_fun (congr_fun (congr_arg nat_trans.app h.inv_hom_id) s_X) s_ι
   exact ULift.up_down _
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_of_cocone CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_homOfCocone
+-/
 
+#print CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone_cooneOfHom /-
 @[simp]
 theorem homOfCocone_cooneOfHom {Y : C} (f : X ⟶ Y) : homOfCocone h (coconeOfHom h f) = f :=
   congr_arg ULift.down (congr_fun (congr_fun (congr_arg NatTrans.app h.hom_inv_id) Y) ⟨f⟩ : _)
 #align category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone_of_hom CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone_cooneOfHom
+-/
 
+#print CategoryTheory.Limits.IsColimit.OfNatIso.colimitCocone /-
 /-- If `F.cocones` is corepresented by `X`, the cocone corresponding to the identity morphism on `X`
 will be a colimit cocone. -/
 def colimitCocone : Cocone F :=
   coconeOfHom h (𝟙 X)
 #align category_theory.limits.is_colimit.of_nat_iso.colimit_cocone CategoryTheory.Limits.IsColimit.OfNatIso.colimitCocone
+-/
 
+#print CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_fac /-
 /-- If `F.cocones` is corepresented by `X`, the cocone corresponding to a morphism `f : Y ⟶ X` is
 the colimit cocone extended by `f`. -/
 theorem coconeOfHom_fac {Y : C} (f : X ⟶ Y) : coconeOfHom h f = (colimitCocone h).extend f :=
@@ -1112,7 +1243,9 @@ theorem coconeOfHom_fac {Y : C} (f : X ⟶ Y) : coconeOfHom h f = (colimitCocone
   rw [congr_fun (congr_arg nat_trans.app t) j]
   rfl
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_fac CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_fac
+-/
 
+#print CategoryTheory.Limits.IsColimit.OfNatIso.cocone_fac /-
 /-- If `F.cocones` is corepresented by `X`, any cocone is the extension of the colimit cocone by the
 corresponding morphism. -/
 theorem cocone_fac (s : Cocone F) : (colimitCocone h).extend (homOfCocone h s) = s :=
@@ -1121,6 +1254,7 @@ theorem cocone_fac (s : Cocone F) : (colimitCocone h).extend (homOfCocone h s) =
   conv_lhs => simp only [hom_of_cocone_of_hom]
   apply (cocone_of_hom_fac _ _).symm
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_fac CategoryTheory.Limits.IsColimit.OfNatIso.cocone_fac
+-/
 
 end OfNatIso
 
@@ -1128,6 +1262,7 @@ section
 
 open OfNatIso
 
+#print CategoryTheory.Limits.IsColimit.ofNatIso /-
 /-- If `F.cocones` is corepresentable, then the cocone corresponding to the identity morphism on
 the representing object is a colimit cocone.
 -/
@@ -1146,6 +1281,7 @@ def ofNatIso {X : C} (h : coyoneda.obj (op X) ⋙ uliftFunctor.{u₁} ≅ F.coco
     rw [cocone_of_hom_fac]
     dsimp [cocone.extend]; cases s; congr with j; exact w j
 #align category_theory.limits.is_colimit.of_nat_iso CategoryTheory.Limits.IsColimit.ofNatIso
+-/
 
 end
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -464,7 +464,7 @@ def homIso' (h : IsLimit t) (W : C) :
       { p : ∀ j, W ⟶ F.obj j // ∀ {j j'} (f : j ⟶ j'), p j ≫ F.map f = p j' } :=
   h.homIso W ≪≫
     { Hom := fun π =>
-        ⟨fun j => π.app j, fun j j' f => by convert← (π.naturality f).symm <;> apply id_comp⟩
+        ⟨fun j => π.app j, fun j j' f => by convert ← (π.naturality f).symm <;> apply id_comp⟩
       inv := fun p =>
         { app := fun j => p.1 j
           naturality' := fun j j' f => by dsimp; rw [id_comp]; exact (p.2 f).symm } }
@@ -481,7 +481,7 @@ def ofFaithful {t : Cone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [F
     uniq := fun s m w => by
       apply G.map_injective; rw [h]
       refine' ht.uniq (G.map_cone s) _ fun j => _
-      convert← congr_arg (fun f => G.map f) (w j)
+      convert ← congr_arg (fun f => G.map f) (w j)
       apply G.map_comp }
 #align category_theory.limits.is_limit.of_faithful CategoryTheory.Limits.IsLimit.ofFaithful
 
@@ -1017,7 +1017,8 @@ def homIso' (h : IsColimit t) (W : C) :
     ULift.{u₁} (t.pt ⟶ W : Type v₃) ≅
       { p : ∀ j, F.obj j ⟶ W // ∀ {j j' : J} (f : j ⟶ j'), F.map f ≫ p j' = p j } :=
   h.homIso W ≪≫
-    { Hom := fun ι => ⟨fun j => ι.app j, fun j j' f => by convert← ι.naturality f <;> apply comp_id⟩
+    { Hom := fun ι =>
+        ⟨fun j => ι.app j, fun j j' f => by convert ← ι.naturality f <;> apply comp_id⟩
       inv := fun p =>
         { app := fun j => p.1 j
           naturality' := fun j j' f => by dsimp; rw [comp_id]; exact p.2 f } }
@@ -1034,7 +1035,7 @@ def ofFaithful {t : Cocone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D)
     uniq := fun s m w => by
       apply G.map_injective; rw [h]
       refine' ht.uniq (G.map_cocone s) _ fun j => _
-      convert← congr_arg (fun f => G.map f) (w j)
+      convert ← congr_arg (fun f => G.map f) (w j)
       apply G.map_comp }
 #align category_theory.limits.is_colimit.of_faithful CategoryTheory.Limits.IsColimit.ofFaithful
 

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

@@ -529,7 +529,7 @@ def homOfCone (s : Cone F) : s.pt ⟶ X :=
 @[simp]
 theorem coneOfHom_homOfCone (s : Cone F) : coneOfHom h (homOfCone h s) = s :=
   by
-  dsimp [cone_of_hom, hom_of_cone]; cases s; congr ; dsimp
+  dsimp [cone_of_hom, hom_of_cone]; cases s; congr; dsimp
   convert congr_fun (congr_fun (congr_arg nat_trans.app h.inv_hom_id) (op s_X)) s_π
   exact ULift.up_down _
 #align category_theory.limits.is_limit.of_nat_iso.cone_of_hom_of_cone CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_homOfCone
@@ -552,8 +552,8 @@ theorem coneOfHom_fac {Y : C} (f : Y ⟶ X) : coneOfHom h f = (limitCone h).exte
   dsimp [cone_of_hom, limit_cone, cone.extend]
   congr with j
   have t := congr_fun (h.hom.naturality f.op) ⟨𝟙 X⟩
-  dsimp at t
-  simp only [comp_id] at t
+  dsimp at t 
+  simp only [comp_id] at t 
   rw [congr_fun (congr_arg nat_trans.app t) j]
   rfl
 #align category_theory.limits.is_limit.of_nat_iso.cone_of_hom_fac CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_fac
@@ -583,7 +583,7 @@ def ofNatIso {X : C} (h : yoneda.obj X ⋙ uliftFunctor.{u₁} ≅ F.cones) : Is
     have h := cone_fac h s
     cases s
     injection h with h₁ h₂
-    simp only [heq_iff_eq] at h₂
+    simp only [heq_iff_eq] at h₂ 
     conv_rhs => rw [← h₂]; rfl
   uniq s m w := by
     rw [← hom_of_cone_of_hom h m]
@@ -1083,7 +1083,7 @@ def homOfCocone (s : Cocone F) : X ⟶ s.pt :=
 @[simp]
 theorem coconeOfHom_homOfCocone (s : Cocone F) : coconeOfHom h (homOfCocone h s) = s :=
   by
-  dsimp [cocone_of_hom, hom_of_cocone]; cases s; congr ; dsimp
+  dsimp [cocone_of_hom, hom_of_cocone]; cases s; congr; dsimp
   convert congr_fun (congr_fun (congr_arg nat_trans.app h.inv_hom_id) s_X) s_ι
   exact ULift.up_down _
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_of_cocone CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_homOfCocone
@@ -1106,8 +1106,8 @@ theorem coconeOfHom_fac {Y : C} (f : X ⟶ Y) : coconeOfHom h f = (colimitCocone
   dsimp [cocone_of_hom, colimit_cocone, cocone.extend]
   congr with j
   have t := congr_fun (h.hom.naturality f) ⟨𝟙 X⟩
-  dsimp at t
-  simp only [id_comp] at t
+  dsimp at t 
+  simp only [id_comp] at t 
   rw [congr_fun (congr_arg nat_trans.app t) j]
   rfl
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_fac CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_fac
@@ -1137,7 +1137,7 @@ def ofNatIso {X : C} (h : coyoneda.obj (op X) ⋙ uliftFunctor.{u₁} ≅ F.coco
     have h := cocone_fac h s
     cases s
     injection h with h₁ h₂
-    simp only [heq_iff_eq] at h₂
+    simp only [heq_iff_eq] at h₂ 
     conv_rhs => rw [← h₂]; rfl
   uniq s m w := by
     rw [← hom_of_cocone_of_hom h m]

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

@@ -91,12 +91,6 @@ def map {F G : J ⥤ C} (s : Cone F) {t : Cone G} (P : IsLimit t) (α : F ⟶ G)
 #align category_theory.limits.is_limit.map CategoryTheory.Limits.IsLimit.map
 -/
 
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 @[simp, reassoc]
 theorem map_π {F G : J ⥤ C} (c : Cone F) {d : Cone G} (hd : IsLimit d) (α : F ⟶ G) (j : J) :
     hd.map c α ≫ d.π.app j = c.π.app j ≫ α.app j :=
@@ -124,24 +118,12 @@ theorem uniq_cone_morphism {s t : Cone F} (h : IsLimit t) {f f' : s ⟶ t} : f =
 #align category_theory.limits.is_limit.uniq_cone_morphism CategoryTheory.Limits.IsLimit.uniq_cone_morphism
 -/
 
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 /-- Restating the definition of a limit cone in terms of the ∃! operator. -/
 theorem existsUnique {t : Cone F} (h : IsLimit t) (s : Cone F) :
     ∃! l : s.pt ⟶ t.pt, ∀ j, l ≫ t.π.app j = s.π.app j :=
   ⟨h.lift s, h.fac s, h.uniq s⟩
 #align category_theory.limits.is_limit.exists_unique CategoryTheory.Limits.IsLimit.existsUnique
 
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 /-- Noncomputably make a colimit cocone from the existence of unique factorizations. -/
 def ofExistsUnique {t : Cone F}
     (ht : ∀ s : Cone F, ∃! l : s.pt ⟶ t.pt, ∀ j, l ≫ t.π.app j = s.π.app j) : IsLimit t := by
@@ -190,24 +172,12 @@ def conePointUniqueUpToIso {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) : s.pt
 #align category_theory.limits.is_limit.cone_point_unique_up_to_iso CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso
 -/
 
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 @[simp, reassoc]
 theorem conePointUniqueUpToIso_hom_comp {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) (j : J) :
     (conePointUniqueUpToIso P Q).Hom ≫ t.π.app j = s.π.app j :=
   (uniqueUpToIso P Q).Hom.w _
 #align category_theory.limits.is_limit.cone_point_unique_up_to_iso_hom_comp CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp
 
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 @[simp, reassoc]
 theorem conePointUniqueUpToIso_inv_comp {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) (j : J) :
     (conePointUniqueUpToIso P Q).inv ≫ s.π.app j = t.π.app j :=
@@ -289,9 +259,6 @@ def ofPointIso {r t : Cone F} (P : IsLimit r) [i : IsIso (P.lift t)] : IsLimit t
 
 variable {t : Cone F}
 
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 theorem hom_lift (h : IsLimit t) {W : C} (m : W ⟶ t.pt) :
     m =
       h.lift
@@ -302,12 +269,6 @@ theorem hom_lift (h : IsLimit t) {W : C} (m : W ⟶ t.pt) :
       π := { app := fun b => m ≫ t.π.app b } } m fun b => rfl
 #align category_theory.limits.is_limit.hom_lift CategoryTheory.Limits.IsLimit.hom_lift
 
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 /-- Two morphisms into a limit are equal if their compositions with
   each cone morphism are equal. -/
 theorem hom_ext (h : IsLimit t) {W : C} {f f' : W ⟶ t.pt}
@@ -315,12 +276,6 @@ theorem hom_ext (h : IsLimit t) {W : C} {f f' : W ⟶ t.pt}
   rw [h.hom_lift f, h.hom_lift f'] <;> congr <;> exact funext w
 #align category_theory.limits.is_limit.hom_ext CategoryTheory.Limits.IsLimit.hom_ext
 
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 /-- Given a right adjoint functor between categories of cones,
 the image of a limit cone is a limit cone.
 -/
@@ -330,12 +285,6 @@ def ofRightAdjoint {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G
     fun s m => (Adjunction.eq_homEquiv_apply _ _ _).2 t.uniq_cone_morphism
 #align category_theory.limits.is_limit.of_right_adjoint CategoryTheory.Limits.IsLimit.ofRightAdjoint
 
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 /-- Given two functors which have equivalent categories of cones, we can transport a limiting cone
 across the equivalence.
 -/
@@ -348,9 +297,6 @@ def ofConeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G 
   right_inv := by tidy
 #align category_theory.limits.is_limit.of_cone_equiv CategoryTheory.Limits.IsLimit.ofConeEquiv
 
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 @[simp]
 theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G ≌ Cone F)
     {c : Cone G} (P : IsLimit (h.Functor.obj c)) (s) :
@@ -360,9 +306,6 @@ theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
   rfl
 #align category_theory.limits.is_limit.of_cone_equiv_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc
 
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 @[simp]
 theorem ofConeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
     (h : Cone G ≌ Cone F) {c : Cone G} (P : IsLimit c) (s) :
@@ -371,12 +314,6 @@ theorem ofConeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K 
   rfl
 #align category_theory.limits.is_limit.of_cone_equiv_symm_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc
 
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 /--
 A cone postcomposed with a natural isomorphism is a limit cone if and only if the original cone is.
 -/
@@ -385,12 +322,6 @@ def postcomposeHomEquiv {F G : J ⥤ C} (α : F ≅ G) (c : Cone F) :
   ofConeEquiv (Cones.postcomposeEquivalence α)
 #align category_theory.limits.is_limit.postcompose_hom_equiv CategoryTheory.Limits.IsLimit.postcomposeHomEquiv
 
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 /-- A cone postcomposed with the inverse of a natural isomorphism is a limit cone if and only if
 the original cone is.
 -/
@@ -399,12 +330,6 @@ def postcomposeInvEquiv {F G : J ⥤ C} (α : F ≅ G) (c : Cone G) :
   postcomposeHomEquiv α.symm c
 #align category_theory.limits.is_limit.postcompose_inv_equiv CategoryTheory.Limits.IsLimit.postcomposeInvEquiv
 
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 /-- Constructing an equivalence `is_limit c ≃ is_limit d` from a natural isomorphism
 between the underlying functors, and then an isomorphism between `c` transported along this and `d`.
 -/
@@ -427,18 +352,12 @@ def conePointsIsoOfNatIso {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit
 #align category_theory.limits.is_limit.cone_points_iso_of_nat_iso CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso
 -/
 
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 @[reassoc]
 theorem conePointsIsoOfNatIso_hom_comp {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit s)
     (Q : IsLimit t) (w : F ≅ G) (j : J) :
     (conePointsIsoOfNatIso P Q w).Hom ≫ t.π.app j = s.π.app j ≫ w.Hom.app j := by simp
 #align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_hom_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp
 
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 @[reassoc]
 theorem conePointsIsoOfNatIso_inv_comp {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit s)
     (Q : IsLimit t) (w : F ≅ G) (j : J) :
@@ -467,24 +386,12 @@ section Equivalence
 
 open CategoryTheory.Equivalence
 
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 /-- If `s : cone F` is a limit cone, so is `s` whiskered by an equivalence `e`.
 -/
 def whiskerEquivalence {s : Cone F} (P : IsLimit s) (e : K ≌ J) : IsLimit (s.whisker e.Functor) :=
   ofRightAdjoint (Cones.whiskeringEquivalence e).Functor P
 #align category_theory.limits.is_limit.whisker_equivalence CategoryTheory.Limits.IsLimit.whiskerEquivalence
 
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 /-- If `s : cone F` whiskered by an equivalence `e` is a limit cone, so is `s`.
 -/
 def ofWhiskerEquivalence {s : Cone F} (e : K ≌ J) (P : IsLimit (s.whisker e.Functor)) : IsLimit s :=
@@ -492,24 +399,12 @@ def ofWhiskerEquivalence {s : Cone F} (e : K ≌ J) (P : IsLimit (s.whisker e.Fu
     (ofRightAdjoint (Cones.whiskeringEquivalence e).inverse P : _)
 #align category_theory.limits.is_limit.of_whisker_equivalence CategoryTheory.Limits.IsLimit.ofWhiskerEquivalence
 
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 /-- Given an equivalence of diagrams `e`, `s` is a limit cone iff `s.whisker e.functor` is.
 -/
 def whiskerEquivalenceEquiv {s : Cone F} (e : K ≌ J) : IsLimit s ≃ IsLimit (s.whisker e.Functor) :=
   ⟨fun h => h.whiskerEquivalence e, ofWhiskerEquivalence e, by tidy, by tidy⟩
 #align category_theory.limits.is_limit.whisker_equivalence_equiv CategoryTheory.Limits.IsLimit.whiskerEquivalenceEquiv
 
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 /-- We can prove two cone points `(s : cone F).X` and `(t.cone G).X` are isomorphic if
 * both cones are limit cones
 * their indexing categories are equivalent via some `e : J ≌ K`,
@@ -537,12 +432,6 @@ def conePointsIsoOfEquivalence {F : J ⥤ C} {s : Cone F} {G : K ⥤ C} {t : Con
 
 end Equivalence
 
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 /-- The universal property of a limit cone: a map `W ⟶ X` is the same as
   a cone on `F` with vertex `W`. -/
 def homIso (h : IsLimit t) (W : C) : ULift.{u₁} (W ⟶ t.pt : Type v₃) ≅ (const J).obj W ⟶ F
@@ -555,36 +444,18 @@ def homIso (h : IsLimit t) (W : C) : ULift.{u₁} (W ⟶ t.pt : Type v₃) ≅ (
   hom_inv_id' := by ext f <;> apply h.hom_ext <;> intro j <;> simp <;> dsimp <;> rfl
 #align category_theory.limits.is_limit.hom_iso CategoryTheory.Limits.IsLimit.homIso
 
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 @[simp]
 theorem homIso_hom (h : IsLimit t) {W : C} (f : ULift.{u₁} (W ⟶ t.pt)) :
     (IsLimit.homIso h W).Hom f = (t.extend f.down).π :=
   rfl
 #align category_theory.limits.is_limit.hom_iso_hom CategoryTheory.Limits.IsLimit.homIso_hom
 
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 /-- The limit of `F` represents the functor taking `W` to
   the set of cones on `F` with vertex `W`. -/
 def natIso (h : IsLimit t) : yoneda.obj t.pt ⋙ uliftFunctor.{u₁} ≅ F.cones :=
   NatIso.ofComponents (fun W => IsLimit.homIso h (unop W)) (by tidy)
 #align category_theory.limits.is_limit.nat_iso CategoryTheory.Limits.IsLimit.natIso
 
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 /-- Another, more explicit, formulation of the universal property of a limit cone.
 See also `hom_iso`.
 -/
@@ -599,12 +470,6 @@ def homIso' (h : IsLimit t) (W : C) :
           naturality' := fun j j' f => by dsimp; rw [id_comp]; exact (p.2 f).symm } }
 #align category_theory.limits.is_limit.hom_iso' CategoryTheory.Limits.IsLimit.homIso'
 
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 /-- If G : C → D is a faithful functor which sends t to a limit cone,
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/
@@ -620,12 +485,6 @@ def ofFaithful {t : Cone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [F
       apply G.map_comp }
 #align category_theory.limits.is_limit.of_faithful CategoryTheory.Limits.IsLimit.ofFaithful
 
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 /-- If `F` and `G` are naturally isomorphic, then `F.map_cone c` being a limit implies
 `G.map_cone c` is also a limit.
 -/
@@ -655,12 +514,6 @@ namespace OfNatIso
 
 variable {X : C} (h : yoneda.obj X ⋙ uliftFunctor.{u₁} ≅ F.cones)
 
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 /-- If `F.cones` is represented by `X`, each morphism `f : Y ⟶ X` gives a cone with cone point
 `Y`. -/
 def coneOfHom {Y : C} (f : Y ⟶ X) : Cone F where
@@ -668,23 +521,11 @@ def coneOfHom {Y : C} (f : Y ⟶ X) : Cone F where
   π := h.Hom.app (op Y) ⟨f⟩
 #align category_theory.limits.is_limit.of_nat_iso.cone_of_hom CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom
 
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 /-- If `F.cones` is represented by `X`, each cone `s` gives a morphism `s.X ⟶ X`. -/
 def homOfCone (s : Cone F) : s.pt ⟶ X :=
   (h.inv.app (op s.pt) s.π).down
 #align category_theory.limits.is_limit.of_nat_iso.hom_of_cone CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone
 
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 @[simp]
 theorem coneOfHom_homOfCone (s : Cone F) : coneOfHom h (homOfCone h s) = s :=
   by
@@ -693,35 +534,17 @@ theorem coneOfHom_homOfCone (s : Cone F) : coneOfHom h (homOfCone h s) = s :=
   exact ULift.up_down _
 #align category_theory.limits.is_limit.of_nat_iso.cone_of_hom_of_cone CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_homOfCone
 
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 @[simp]
 theorem homOfCone_coneOfHom {Y : C} (f : Y ⟶ X) : homOfCone h (coneOfHom h f) = f :=
   congr_arg ULift.down (congr_fun (congr_fun (congr_arg NatTrans.app h.hom_inv_id) (op Y)) ⟨f⟩ : _)
 #align category_theory.limits.is_limit.of_nat_iso.hom_of_cone_of_hom CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone_coneOfHom
 
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 /-- If `F.cones` is represented by `X`, the cone corresponding to the identity morphism on `X`
 will be a limit cone. -/
 def limitCone : Cone F :=
   coneOfHom h (𝟙 X)
 #align category_theory.limits.is_limit.of_nat_iso.limit_cone CategoryTheory.Limits.IsLimit.OfNatIso.limitCone
 
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 /-- If `F.cones` is represented by `X`, the cone corresponding to a morphism `f : Y ⟶ X` is
 the limit cone extended by `f`. -/
 theorem coneOfHom_fac {Y : C} (f : Y ⟶ X) : coneOfHom h f = (limitCone h).extend f :=
@@ -735,12 +558,6 @@ theorem coneOfHom_fac {Y : C} (f : Y ⟶ X) : coneOfHom h f = (limitCone h).exte
   rfl
 #align category_theory.limits.is_limit.of_nat_iso.cone_of_hom_fac CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_fac
 
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 /-- If `F.cones` is represented by `X`, any cone is the extension of the limit cone by the
 corresponding morphism. -/
 theorem cone_fac (s : Cone F) : (limitCone h).extend (homOfCone h s) = s :=
@@ -756,12 +573,6 @@ section
 
 open OfNatIso
 
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 /-- If `F.cones` is representable, then the cone corresponding to the identity morphism on
 the representing object is a limit cone.
 -/
@@ -823,9 +634,6 @@ def map {F G : J ⥤ C} {s : Cocone F} (P : IsColimit s) (t : Cocone G) (α : F
 #align category_theory.limits.is_colimit.map CategoryTheory.Limits.IsColimit.map
 -/
 
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 @[simp, reassoc]
 theorem ι_map {F G : J ⥤ C} {c : Cocone F} (hc : IsColimit c) (d : Cocone G) (α : F ⟶ G) (j : J) :
     c.ι.app j ≫ IsColimit.map hc d α = α.app j ≫ d.ι.app j :=
@@ -854,24 +662,12 @@ theorem uniq_cocone_morphism {s t : Cocone F} (h : IsColimit t) {f f' : t ⟶ s}
 #align category_theory.limits.is_colimit.uniq_cocone_morphism CategoryTheory.Limits.IsColimit.uniq_cocone_morphism
 -/
 
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 /-- Restating the definition of a colimit cocone in terms of the ∃! operator. -/
 theorem existsUnique {t : Cocone F} (h : IsColimit t) (s : Cocone F) :
     ∃! d : t.pt ⟶ s.pt, ∀ j, t.ι.app j ≫ d = s.ι.app j :=
   ⟨h.desc s, h.fac s, h.uniq s⟩
 #align category_theory.limits.is_colimit.exists_unique CategoryTheory.Limits.IsColimit.existsUnique
 
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 /-- Noncomputably make a colimit cocone from the existence of unique factorizations. -/
 def ofExistsUnique {t : Cocone F}
     (ht : ∀ s : Cocone F, ∃! d : t.pt ⟶ s.pt, ∀ j, t.ι.app j ≫ d = s.ι.app j) : IsColimit t := by
@@ -920,24 +716,12 @@ def coconePointUniqueUpToIso {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t
 #align category_theory.limits.is_colimit.cocone_point_unique_up_to_iso CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso
 -/
 
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 @[simp, reassoc]
 theorem comp_coconePointUniqueUpToIso_hom {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t)
     (j : J) : s.ι.app j ≫ (coconePointUniqueUpToIso P Q).Hom = t.ι.app j :=
   (uniqueUpToIso P Q).Hom.w _
 #align category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_hom CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom
 
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 @[simp, reassoc]
 theorem comp_coconePointUniqueUpToIso_inv {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t)
     (j : J) : t.ι.app j ≫ (coconePointUniqueUpToIso P Q).inv = s.ι.app j :=
@@ -1018,9 +802,6 @@ def ofPointIso {r t : Cocone F} (P : IsColimit r) [i : IsIso (P.desc t)] : IsCol
 
 variable {t : Cocone F}
 
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 theorem hom_desc (h : IsColimit t) {W : C} (m : t.pt ⟶ W) :
     m =
       h.desc
@@ -1036,9 +817,6 @@ theorem hom_desc (h : IsColimit t) {W : C} (m : t.pt ⟶ W) :
     m fun b => rfl
 #align category_theory.limits.is_colimit.hom_desc CategoryTheory.Limits.IsColimit.hom_desc
 
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 /-- Two morphisms out of a colimit are equal if their compositions with
   each cocone morphism are equal. -/
 theorem hom_ext (h : IsColimit t) {W : C} {f f' : t.pt ⟶ W}
@@ -1046,12 +824,6 @@ theorem hom_ext (h : IsColimit t) {W : C} {f f' : t.pt ⟶ W}
   rw [h.hom_desc f, h.hom_desc f'] <;> congr <;> exact funext w
 #align category_theory.limits.is_colimit.hom_ext CategoryTheory.Limits.IsColimit.hom_ext
 
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 /-- Given a left adjoint functor between categories of cocones,
 the image of a colimit cocone is a colimit cocone.
 -/
@@ -1062,12 +834,6 @@ def ofLeftAdjoint {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cocone
     (Adjunction.homEquiv_apply_eq _ _ _).1 t.uniq_cocone_morphism
 #align category_theory.limits.is_colimit.of_left_adjoint CategoryTheory.Limits.IsColimit.ofLeftAdjoint
 
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 /-- Given two functors which have equivalent categories of cocones,
 we can transport a colimiting cocone across the equivalence.
 -/
@@ -1080,9 +846,6 @@ def ofCoconeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cocone
   right_inv := by tidy
 #align category_theory.limits.is_colimit.of_cocone_equiv CategoryTheory.Limits.IsColimit.ofCoconeEquiv
 
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 @[simp]
 theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
     (h : Cocone G ≌ Cocone F) {c : Cocone G} (P : IsColimit (h.Functor.obj c)) (s) :
@@ -1092,9 +855,6 @@ theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤
   rfl
 #align category_theory.limits.is_colimit.of_cocone_equiv_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc
 
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 @[simp]
 theorem ofCoconeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
     (h : Cocone G ≌ Cocone F) {c : Cocone G} (P : IsColimit c) (s) :
@@ -1103,12 +863,6 @@ theorem ofCoconeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K
   rfl
 #align category_theory.limits.is_colimit.of_cocone_equiv_symm_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc
 
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 /-- A cocone precomposed with a natural isomorphism is a colimit cocone
 if and only if the original cocone is.
 -/
@@ -1117,12 +871,6 @@ def precomposeHomEquiv {F G : J ⥤ C} (α : F ≅ G) (c : Cocone G) :
   ofCoconeEquiv (Cocones.precomposeEquivalence α)
 #align category_theory.limits.is_colimit.precompose_hom_equiv CategoryTheory.Limits.IsColimit.precomposeHomEquiv
 
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 /-- A cocone precomposed with the inverse of a natural isomorphism is a colimit cocone
 if and only if the original cocone is.
 -/
@@ -1131,12 +879,6 @@ def precomposeInvEquiv {F G : J ⥤ C} (α : F ≅ G) (c : Cocone F) :
   precomposeHomEquiv α.symm c
 #align category_theory.limits.is_colimit.precompose_inv_equiv CategoryTheory.Limits.IsColimit.precomposeInvEquiv
 
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 /-- Constructing an equivalence `is_colimit c ≃ is_colimit d` from a natural isomorphism
 between the underlying functors, and then an isomorphism between `c` transported along this and `d`.
 -/
@@ -1160,18 +902,12 @@ def coconePointsIsoOfNatIso {F G : J ⥤ C} {s : Cocone F} {t : Cocone G} (P : I
 #align category_theory.limits.is_colimit.cocone_points_iso_of_nat_iso CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso
 -/
 
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 @[reassoc]
 theorem comp_coconePointsIsoOfNatIso_hom {F G : J ⥤ C} {s : Cocone F} {t : Cocone G}
     (P : IsColimit s) (Q : IsColimit t) (w : F ≅ G) (j : J) :
     s.ι.app j ≫ (coconePointsIsoOfNatIso P Q w).Hom = w.Hom.app j ≫ t.ι.app j := by simp
 #align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_hom CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom
 
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 @[reassoc]
 theorem comp_coconePointsIsoOfNatIso_inv {F G : J ⥤ C} {s : Cocone F} {t : Cocone G}
     (P : IsColimit s) (Q : IsColimit t) (w : F ≅ G) (j : J) :
@@ -1200,12 +936,6 @@ section Equivalence
 
 open CategoryTheory.Equivalence
 
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 /-- If `s : cocone F` is a colimit cocone, so is `s` whiskered by an equivalence `e`.
 -/
 def whiskerEquivalence {s : Cocone F} (P : IsColimit s) (e : K ≌ J) :
@@ -1213,12 +943,6 @@ def whiskerEquivalence {s : Cocone F} (P : IsColimit s) (e : K ≌ J) :
   ofLeftAdjoint (Cocones.whiskeringEquivalence e).Functor P
 #align category_theory.limits.is_colimit.whisker_equivalence CategoryTheory.Limits.IsColimit.whiskerEquivalence
 
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 /-- If `s : cocone F` whiskered by an equivalence `e` is a colimit cocone, so is `s`.
 -/
 def ofWhiskerEquivalence {s : Cocone F} (e : K ≌ J) (P : IsColimit (s.whisker e.Functor)) :
@@ -1227,12 +951,6 @@ def ofWhiskerEquivalence {s : Cocone F} (e : K ≌ J) (P : IsColimit (s.whisker
     (ofLeftAdjoint (Cocones.whiskeringEquivalence e).inverse P : _)
 #align category_theory.limits.is_colimit.of_whisker_equivalence CategoryTheory.Limits.IsColimit.ofWhiskerEquivalence
 
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 /-- Given an equivalence of diagrams `e`, `s` is a colimit cocone iff `s.whisker e.functor` is.
 -/
 def whiskerEquivalenceEquiv {s : Cocone F} (e : K ≌ J) :
@@ -1240,12 +958,6 @@ def whiskerEquivalenceEquiv {s : Cocone F} (e : K ≌ J) :
   ⟨fun h => h.whiskerEquivalence e, ofWhiskerEquivalence e, by tidy, by tidy⟩
 #align category_theory.limits.is_colimit.whisker_equivalence_equiv CategoryTheory.Limits.IsColimit.whiskerEquivalenceEquiv
 
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 /-- We can prove two cocone points `(s : cocone F).X` and `(t.cocone G).X` are isomorphic if
 * both cocones are colimit cocones
 * their indexing categories are equivalent via some `e : J ≌ K`,
@@ -1274,12 +986,6 @@ def coconePointsIsoOfEquivalence {F : J ⥤ C} {s : Cocone F} {G : K ⥤ C} {t :
 
 end Equivalence
 
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 /-- The universal property of a colimit cocone: a map `X ⟶ W` is the same as
   a cocone on `F` with vertex `W`. -/
 def homIso (h : IsColimit t) (W : C) : ULift.{u₁} (t.pt ⟶ W : Type v₃) ≅ F ⟶ (const J).obj W
@@ -1292,36 +998,18 @@ def homIso (h : IsColimit t) (W : C) : ULift.{u₁} (t.pt ⟶ W : Type v₃) ≅
   hom_inv_id' := by ext f <;> apply h.hom_ext <;> intro j <;> simp <;> dsimp <;> rfl
 #align category_theory.limits.is_colimit.hom_iso CategoryTheory.Limits.IsColimit.homIso
 
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 @[simp]
 theorem homIso_hom (h : IsColimit t) {W : C} (f : ULift (t.pt ⟶ W)) :
     (IsColimit.homIso h W).Hom f = (t.extend f.down).ι :=
   rfl
 #align category_theory.limits.is_colimit.hom_iso_hom CategoryTheory.Limits.IsColimit.homIso_hom
 
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 /-- The colimit of `F` represents the functor taking `W` to
   the set of cocones on `F` with vertex `W`. -/
 def natIso (h : IsColimit t) : coyoneda.obj (op t.pt) ⋙ uliftFunctor.{u₁} ≅ F.cocones :=
   NatIso.ofComponents (IsColimit.homIso h) (by intros <;> ext <;> dsimp <;> rw [← assoc] <;> rfl)
 #align category_theory.limits.is_colimit.nat_iso CategoryTheory.Limits.IsColimit.natIso
 
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 /-- Another, more explicit, formulation of the universal property of a colimit cocone.
 See also `hom_iso`.
 -/
@@ -1335,12 +1023,6 @@ def homIso' (h : IsColimit t) (W : C) :
           naturality' := fun j j' f => by dsimp; rw [comp_id]; exact p.2 f } }
 #align category_theory.limits.is_colimit.hom_iso' CategoryTheory.Limits.IsColimit.homIso'
 
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 /-- If G : C → D is a faithful functor which sends t to a colimit cocone,
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/
@@ -1356,12 +1038,6 @@ def ofFaithful {t : Cocone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D)
       apply G.map_comp }
 #align category_theory.limits.is_colimit.of_faithful CategoryTheory.Limits.IsColimit.ofFaithful
 
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 /-- If `F` and `G` are naturally isomorphic, then `F.map_cone c` being a colimit implies
 `G.map_cone c` is also a colimit.
 -/
@@ -1391,12 +1067,6 @@ namespace OfNatIso
 
 variable {X : C} (h : coyoneda.obj (op X) ⋙ uliftFunctor.{u₁} ≅ F.cocones)
 
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 /-- If `F.cocones` is corepresented by `X`, each morphism `f : X ⟶ Y` gives a cocone with cone
 point `Y`. -/
 def coconeOfHom {Y : C} (f : X ⟶ Y) : Cocone F
@@ -1405,23 +1075,11 @@ def coconeOfHom {Y : C} (f : X ⟶ Y) : Cocone F
   ι := h.Hom.app Y ⟨f⟩
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom
 
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 /-- If `F.cocones` is corepresented by `X`, each cocone `s` gives a morphism `X ⟶ s.X`. -/
 def homOfCocone (s : Cocone F) : X ⟶ s.pt :=
   (h.inv.app s.pt s.ι).down
 #align category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone
 
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 @[simp]
 theorem coconeOfHom_homOfCocone (s : Cocone F) : coconeOfHom h (homOfCocone h s) = s :=
   by
@@ -1430,35 +1088,17 @@ theorem coconeOfHom_homOfCocone (s : Cocone F) : coconeOfHom h (homOfCocone h s)
   exact ULift.up_down _
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_of_cocone CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_homOfCocone
 
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 @[simp]
 theorem homOfCocone_cooneOfHom {Y : C} (f : X ⟶ Y) : homOfCocone h (coconeOfHom h f) = f :=
   congr_arg ULift.down (congr_fun (congr_fun (congr_arg NatTrans.app h.hom_inv_id) Y) ⟨f⟩ : _)
 #align category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone_of_hom CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone_cooneOfHom
 
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 /-- If `F.cocones` is corepresented by `X`, the cocone corresponding to the identity morphism on `X`
 will be a colimit cocone. -/
 def colimitCocone : Cocone F :=
   coconeOfHom h (𝟙 X)
 #align category_theory.limits.is_colimit.of_nat_iso.colimit_cocone CategoryTheory.Limits.IsColimit.OfNatIso.colimitCocone
 
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 /-- If `F.cocones` is corepresented by `X`, the cocone corresponding to a morphism `f : Y ⟶ X` is
 the colimit cocone extended by `f`. -/
 theorem coconeOfHom_fac {Y : C} (f : X ⟶ Y) : coconeOfHom h f = (colimitCocone h).extend f :=
@@ -1472,12 +1112,6 @@ theorem coconeOfHom_fac {Y : C} (f : X ⟶ Y) : coconeOfHom h f = (colimitCocone
   rfl
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_fac CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_fac
 
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 /-- If `F.cocones` is corepresented by `X`, any cocone is the extension of the colimit cocone by the
 corresponding morphism. -/
 theorem cocone_fac (s : Cocone F) : (colimitCocone h).extend (homOfCocone h s) = s :=
@@ -1493,12 +1127,6 @@ section
 
 open OfNatIso
 
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 /-- If `F.cocones` is corepresentable, then the cocone corresponding to the identity morphism on
 the representing object is a colimit cocone.
 -/

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

@@ -144,10 +144,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_exists_unique CategoryTheory.Limits.IsLimit.ofExistsUniqueₓ'. -/
 /-- Noncomputably make a colimit cocone from the existence of unique factorizations. -/
 def ofExistsUnique {t : Cone F}
-    (ht : ∀ s : Cone F, ∃! l : s.pt ⟶ t.pt, ∀ j, l ≫ t.π.app j = s.π.app j) : IsLimit t :=
-  by
-  choose s hs hs' using ht
-  exact ⟨s, hs, hs'⟩
+    (ht : ∀ s : Cone F, ∃! l : s.pt ⟶ t.pt, ∀ j, l ≫ t.π.app j = s.π.app j) : IsLimit t := by
+  choose s hs hs' using ht; exact ⟨s, hs, hs'⟩
 #align category_theory.limits.is_limit.of_exists_unique CategoryTheory.Limits.IsLimit.ofExistsUnique
 
 #print CategoryTheory.Limits.IsLimit.mkConeMorphism /-
@@ -534,9 +532,7 @@ def conePointsIsoOfEquivalence {F : J ⥤ C} {s : Cone F} {G : K ⥤ C} {t : Con
         assoc, id_comp, inv_fun_id_assoc_hom_app, fac_assoc, nat_trans.comp_app]
       rw [counit_app_functor, ← functor.comp_map, w.hom.naturality]
       simp
-    inv_hom_id' := by
-      apply hom_ext Q
-      tidy }
+    inv_hom_id' := by apply hom_ext Q; tidy }
 #align category_theory.limits.is_limit.cone_points_iso_of_equivalence CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence
 
 end Equivalence
@@ -878,10 +874,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_exists_unique CategoryTheory.Limits.IsColimit.ofExistsUniqueₓ'. -/
 /-- Noncomputably make a colimit cocone from the existence of unique factorizations. -/
 def ofExistsUnique {t : Cocone F}
-    (ht : ∀ s : Cocone F, ∃! d : t.pt ⟶ s.pt, ∀ j, t.ι.app j ≫ d = s.ι.app j) : IsColimit t :=
-  by
-  choose s hs hs' using ht
-  exact ⟨s, hs, hs'⟩
+    (ht : ∀ s : Cocone F, ∃! d : t.pt ⟶ s.pt, ∀ j, t.ι.app j ≫ d = s.ι.app j) : IsColimit t := by
+  choose s hs hs' using ht; exact ⟨s, hs, hs'⟩
 #align category_theory.limits.is_colimit.of_exists_unique CategoryTheory.Limits.IsColimit.ofExistsUnique
 
 #print CategoryTheory.Limits.IsColimit.mkCoconeMorphism /-
@@ -1275,9 +1269,7 @@ def coconePointsIsoOfEquivalence {F : J ⥤ C} {s : Cocone F} {G : K ⥤ C} {t :
       rw [counit_inv_app_functor, ← functor.comp_map, ← w.inv.naturality_assoc]
       dsimp
       simp
-    inv_hom_id' := by
-      apply hom_ext Q
-      tidy }
+    inv_hom_id' := by apply hom_ext Q; tidy }
 #align category_theory.limits.is_colimit.cocone_points_iso_of_equivalence CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence
 
 end Equivalence

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

@@ -292,10 +292,7 @@ def ofPointIso {r t : Cone F} (P : IsLimit r) [i : IsIso (P.lift t)] : IsLimit t
 variable {t : Cone F}
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.hom_lift CategoryTheory.Limits.IsLimit.hom_liftₓ'. -/
 theorem hom_lift (h : IsLimit t) {W : C} (m : W ⟶ t.pt) :
     m =
@@ -354,10 +351,7 @@ def ofConeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G 
 #align category_theory.limits.is_limit.of_cone_equiv CategoryTheory.Limits.IsLimit.ofConeEquiv
 
 /- warning: category_theory.limits.is_limit.of_cone_equiv_apply_desc -> CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_cone_equiv_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_descₓ'. -/
 @[simp]
 theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G ≌ Cone F)
@@ -369,10 +363,7 @@ theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
 #align category_theory.limits.is_limit.of_cone_equiv_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc
 
 /- warning: category_theory.limits.is_limit.of_cone_equiv_symm_apply_desc -> CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_cone_equiv_symm_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_descₓ'. -/
 @[simp]
 theorem ofConeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
@@ -439,10 +430,7 @@ def conePointsIsoOfNatIso {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit
 -/
 
 /- warning: category_theory.limits.is_limit.cone_points_iso_of_nat_iso_hom_comp -> CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_hom_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_compₓ'. -/
 @[reassoc]
 theorem conePointsIsoOfNatIso_hom_comp {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit s)
@@ -451,10 +439,7 @@ theorem conePointsIsoOfNatIso_hom_comp {F G : J ⥤ C} {s : Cone F} {t : Cone G}
 #align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_hom_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_inv_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_compₓ'. -/
 @[reassoc]
 theorem conePointsIsoOfNatIso_inv_comp {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit s)
@@ -843,10 +828,7 @@ def map {F G : J ⥤ C} {s : Cocone F} (P : IsColimit s) (t : Cocone G) (α : F
 -/
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.ι_map CategoryTheory.Limits.IsColimit.ι_mapₓ'. -/
 @[simp, reassoc]
 theorem ι_map {F G : J ⥤ C} {c : Cocone F} (hc : IsColimit c) (d : Cocone G) (α : F ⟶ G) (j : J) :
@@ -1043,10 +1025,7 @@ def ofPointIso {r t : Cocone F} (P : IsColimit r) [i : IsIso (P.desc t)] : IsCol
 variable {t : Cocone F}
 
 /- warning: category_theory.limits.is_colimit.hom_desc -> CategoryTheory.Limits.IsColimit.hom_desc is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.hom_desc CategoryTheory.Limits.IsColimit.hom_descₓ'. -/
 theorem hom_desc (h : IsColimit t) {W : C} (m : t.pt ⟶ W) :
     m =
@@ -1064,10 +1043,7 @@ theorem hom_desc (h : IsColimit t) {W : C} (m : t.pt ⟶ W) :
 #align category_theory.limits.is_colimit.hom_desc CategoryTheory.Limits.IsColimit.hom_desc
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.hom_ext CategoryTheory.Limits.IsColimit.hom_extₓ'. -/
 /-- Two morphisms out of a colimit are equal if their compositions with
   each cocone morphism are equal. -/
@@ -1111,10 +1087,7 @@ def ofCoconeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cocone
 #align category_theory.limits.is_colimit.of_cocone_equiv CategoryTheory.Limits.IsColimit.ofCoconeEquiv
 
 /- warning: category_theory.limits.is_colimit.of_cocone_equiv_apply_desc -> CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_cocone_equiv_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_descₓ'. -/
 @[simp]
 theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
@@ -1126,10 +1099,7 @@ theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤
 #align category_theory.limits.is_colimit.of_cocone_equiv_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc
 
 /- warning: category_theory.limits.is_colimit.of_cocone_equiv_symm_apply_desc -> CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_cocone_equiv_symm_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_descₓ'. -/
 @[simp]
 theorem ofCoconeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
@@ -1197,10 +1167,7 @@ def coconePointsIsoOfNatIso {F G : J ⥤ C} {s : Cocone F} {t : Cocone G} (P : I
 -/
 
 /- warning: category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_hom -> CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_hom CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_homₓ'. -/
 @[reassoc]
 theorem comp_coconePointsIsoOfNatIso_hom {F G : J ⥤ C} {s : Cocone F} {t : Cocone G}
@@ -1209,10 +1176,7 @@ theorem comp_coconePointsIsoOfNatIso_hom {F G : J ⥤ C} {s : Cocone F} {t : Coc
 #align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_hom CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom
 
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u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s))) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 G F (CategoryTheory.Iso.inv.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G w) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_inv CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_invₓ'. -/
 @[reassoc]
 theorem comp_coconePointsIsoOfNatIso_inv {F G : J ⥤ C} {s : Cocone F} {t : Cocone G}

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -71,7 +71,7 @@ structure IsLimit (t : Cone F) where
 
 restate_axiom is_limit.fac'
 
-attribute [simp, reassoc.1] is_limit.fac
+attribute [simp, reassoc] is_limit.fac
 
 restate_axiom is_limit.uniq'
 
@@ -97,7 +97,7 @@ lean 3 declaration is
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} (c : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) {d : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G} (hd : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d) (α : Quiver.Hom.{max (succ u3) (succ u2), max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j) (CategoryTheory.Limits.IsLimit.map.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G c d hd α) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d)) G (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c))) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G α j))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.map_π CategoryTheory.Limits.IsLimit.map_πₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem map_π {F G : J ⥤ C} (c : Cone F) {d : Cone G} (hd : IsLimit d) (α : F ⟶ G) (j : J) :
     hd.map c α ≫ d.π.app j = c.π.app j ≫ α.app j :=
   fac _ _ _
@@ -198,7 +198,7 @@ lean 3 declaration is
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (P : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (CategoryTheory.Iso.hom.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s t P Q)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_point_unique_up_to_iso_hom_comp CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_compₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem conePointUniqueUpToIso_hom_comp {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) (j : J) :
     (conePointUniqueUpToIso P Q).Hom ≫ t.π.app j = s.π.app j :=
   (uniqueUpToIso P Q).Hom.w _
@@ -210,14 +210,14 @@ lean 3 declaration is
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (P : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (CategoryTheory.Iso.inv.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s t P Q)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_point_unique_up_to_iso_inv_comp CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_compₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem conePointUniqueUpToIso_inv_comp {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) (j : J) :
     (conePointUniqueUpToIso P Q).inv ≫ s.π.app j = t.π.app j :=
   (uniqueUpToIso P Q).inv.w _
 #align category_theory.limits.is_limit.cone_point_unique_up_to_iso_inv_comp CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp
 
 #print CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_hom /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem lift_comp_conePointUniqueUpToIso_hom {r s t : Cone F} (P : IsLimit s) (Q : IsLimit t) :
     P.lift r ≫ (conePointUniqueUpToIso P Q).Hom = Q.lift r :=
   Q.uniq _ _ (by simp)
@@ -225,7 +225,7 @@ theorem lift_comp_conePointUniqueUpToIso_hom {r s t : Cone F} (P : IsLimit s) (Q
 -/
 
 #print CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_inv /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem lift_comp_conePointUniqueUpToIso_inv {r s t : Cone F} (P : IsLimit s) (Q : IsLimit t) :
     Q.lift r ≫ (conePointUniqueUpToIso P Q).inv = P.lift r :=
   P.uniq _ _ (by simp)
@@ -444,7 +444,7 @@ lean 3 declaration is
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G} (P : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (w : CategoryTheory.Iso.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j) (CategoryTheory.Iso.hom.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G s t P Q w)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t)) G (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C 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(CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G (CategoryTheory.Iso.hom.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G w) j))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_hom_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_compₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem conePointsIsoOfNatIso_hom_comp {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit s)
     (Q : IsLimit t) (w : F ≅ G) (j : J) :
     (conePointsIsoOfNatIso P Q w).Hom ≫ t.π.app j = s.π.app j ≫ w.Hom.app j := by simp
@@ -456,14 +456,14 @@ lean 3 declaration is
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G} (P : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (w : CategoryTheory.Iso.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (CategoryTheory.Iso.inv.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G s t P Q w)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t))) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t)) G (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 G F (CategoryTheory.Iso.inv.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G w) j))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_inv_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_compₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem conePointsIsoOfNatIso_inv_comp {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit s)
     (Q : IsLimit t) (w : F ≅ G) (j : J) :
     (conePointsIsoOfNatIso P Q w).inv ≫ s.π.app j = t.π.app j ≫ w.inv.app j := by simp
 #align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_inv_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp
 
 #print CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom /-
-@[reassoc.1]
+@[reassoc]
 theorem lift_comp_conePointsIsoOfNatIso_hom {F G : J ⥤ C} {r s : Cone F} {t : Cone G}
     (P : IsLimit s) (Q : IsLimit t) (w : F ≅ G) :
     P.lift r ≫ (conePointsIsoOfNatIso P Q w).Hom = Q.map r w.Hom :=
@@ -472,7 +472,7 @@ theorem lift_comp_conePointsIsoOfNatIso_hom {F G : J ⥤ C} {r s : Cone F} {t :
 -/
 
 #print CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv /-
-@[reassoc.1]
+@[reassoc]
 theorem lift_comp_conePointsIsoOfNatIso_inv {F G : J ⥤ C} {r s : Cone G} {t : Cone F}
     (P : IsLimit t) (Q : IsLimit s) (w : F ≅ G) :
     Q.lift r ≫ (conePointsIsoOfNatIso P Q w).inv = P.map r w.inv :=
@@ -822,7 +822,7 @@ structure IsColimit (t : Cocone F) where
 
 restate_axiom is_colimit.fac'
 
-attribute [simp, reassoc.1] is_colimit.fac
+attribute [simp, reassoc] is_colimit.fac
 
 restate_axiom is_colimit.uniq'
 
@@ -848,7 +848,7 @@ lean 3 declaration is
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {c : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (hc : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c) (d : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) (α : Quiver.Hom.{max (succ u3) (succ u2), max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c))) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c) j) (CategoryTheory.Limits.IsColimit.map.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G c hc d α)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d))) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G α j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 G (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d) j))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.ι_map CategoryTheory.Limits.IsColimit.ι_mapₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem ι_map {F G : J ⥤ C} {c : Cocone F} (hc : IsColimit c) (d : Cocone G) (α : F ⟶ G) (j : J) :
     c.ι.app j ≫ IsColimit.map hc d α = α.app j ≫ d.ι.app j :=
   fac _ _ _
@@ -950,7 +950,7 @@ lean 3 declaration is
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (P : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s))) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j) (CategoryTheory.Iso.hom.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s t P Q))) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_hom CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_homₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem comp_coconePointUniqueUpToIso_hom {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t)
     (j : J) : s.ι.app j ≫ (coconePointUniqueUpToIso P Q).Hom = t.ι.app j :=
   (uniqueUpToIso P Q).Hom.w _
@@ -962,14 +962,14 @@ lean 3 declaration is
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (P : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j) (CategoryTheory.Iso.inv.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s t P Q))) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_inv CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_invₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem comp_coconePointUniqueUpToIso_inv {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t)
     (j : J) : t.ι.app j ≫ (coconePointUniqueUpToIso P Q).inv = s.ι.app j :=
   (uniqueUpToIso P Q).inv.w _
 #align category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_inv CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv
 
 #print CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem coconePointUniqueUpToIso_hom_desc {r s t : Cocone F} (P : IsColimit s) (Q : IsColimit t) :
     (coconePointUniqueUpToIso P Q).Hom ≫ Q.desc r = P.desc r :=
   P.uniq _ _ (by simp)
@@ -977,7 +977,7 @@ theorem coconePointUniqueUpToIso_hom_desc {r s t : Cocone F} (P : IsColimit s) (
 -/
 
 #print CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_inv_desc /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem coconePointUniqueUpToIso_inv_desc {r s t : Cocone F} (P : IsColimit s) (Q : IsColimit t) :
     (coconePointUniqueUpToIso P Q).inv ≫ P.desc r = Q.desc r :=
   Q.uniq _ _ (by simp)
@@ -1202,7 +1202,7 @@ lean 3 declaration is
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G} (P : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (w : CategoryTheory.Iso.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s))) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j) (CategoryTheory.Iso.hom.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G s t P Q w))) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t))) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G (CategoryTheory.Iso.hom.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G w) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 G (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) j))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_hom CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_homₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem comp_coconePointsIsoOfNatIso_hom {F G : J ⥤ C} {s : Cocone F} {t : Cocone G}
     (P : IsColimit s) (Q : IsColimit t) (w : F ≅ G) (j : J) :
     s.ι.app j ≫ (coconePointsIsoOfNatIso P Q w).Hom = w.Hom.app j ≫ t.ι.app j := by simp
@@ -1214,14 +1214,14 @@ lean 3 declaration is
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G} (P : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (w : CategoryTheory.Iso.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t))) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 G (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) j) (CategoryTheory.Iso.inv.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G s t P Q w))) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s))) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 G F (CategoryTheory.Iso.inv.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G w) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_inv CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_invₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem comp_coconePointsIsoOfNatIso_inv {F G : J ⥤ C} {s : Cocone F} {t : Cocone G}
     (P : IsColimit s) (Q : IsColimit t) (w : F ≅ G) (j : J) :
     t.ι.app j ≫ (coconePointsIsoOfNatIso P Q w).inv = w.inv.app j ≫ s.ι.app j := by simp
 #align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_inv CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv
 
 #print CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc /-
-@[reassoc.1]
+@[reassoc]
 theorem coconePointsIsoOfNatIso_hom_desc {F G : J ⥤ C} {s : Cocone F} {r t : Cocone G}
     (P : IsColimit s) (Q : IsColimit t) (w : F ≅ G) :
     (coconePointsIsoOfNatIso P Q w).Hom ≫ Q.desc r = P.map _ w.Hom :=
@@ -1230,7 +1230,7 @@ theorem coconePointsIsoOfNatIso_hom_desc {F G : J ⥤ C} {s : Cocone F} {r t : C
 -/
 
 #print CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc /-
-@[reassoc.1]
+@[reassoc]
 theorem coconePointsIsoOfNatIso_inv_desc {F G : J ⥤ C} {s : Cocone G} {r t : Cocone F}
     (P : IsColimit t) (Q : IsColimit s) (w : F ≅ G) :
     (coconePointsIsoOfNatIso P Q w).inv ≫ P.desc r = Q.map _ w.inv :=

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

@@ -357,7 +357,7 @@ def ofConeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G 
 lean 3 declaration is
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 but is expected to have type
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G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h) (CategoryTheory.Equivalence.inverse.{u4, u3, max (max u6 u8) u4, max (max u5 u7) u3} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h)) (CategoryTheory.Functor.id.{u4, max (max u6 u8) u4} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G)) (CategoryTheory.Iso.inv.{max (max u6 u8) u4, max (max u6 u8) u4} (CategoryTheory.Functor.{u4, u4, max (max u6 u8) u4, max (max u6 u8) u4} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G)) (CategoryTheory.Functor.category.{u4, u4, max (max u6 u8) u4, max (max u6 u8) u4} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G)) (CategoryTheory.Functor.id.{u4, max (max u6 u8) u4} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G)) (CategoryTheory.Functor.comp.{u4, u3, u4, max (max u6 u8) u4, max (max u5 u7) u3, max (max u6 u8) u4} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Equivalence.functor.{u4, u3, max (max u6 u8) u4, max (max u5 u7) u3} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h) (CategoryTheory.Equivalence.inverse.{u4, u3, max (max u6 u8) u4, max (max u5 u7) u3} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h)) (CategoryTheory.Equivalence.unitIso.{u4, u3, max (max u6 u8) u4, max (max u5 u7) u3} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h)) c)))
+  forall {J : Type.{u5}} [_inst_1 : CategoryTheory.Category.{u1, u5} J] {K : Type.{u6}} [_inst_2 : CategoryTheory.Category.{u2, u6} K] {C : Type.{u7}} [_inst_3 : CategoryTheory.Category.{u3, u7} C] {F : CategoryTheory.Functor.{u1, u3, u5, u7} J _inst_1 C _inst_3} {D : Type.{u8}} [_inst_4 : CategoryTheory.Category.{u4, u8} D] {G : CategoryTheory.Functor.{u2, u4, u6, u8} K _inst_2 D _inst_4} (h : CategoryTheory.Equivalence.{u4, u3, max (max u8 u6) u4, max (max u7 u5) u3} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F)) {c : CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G} (P : CategoryTheory.Limits.IsLimit.{u1, u3, u5, u7} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u4, succ u3, max (max u6 u8) u4, max (max u5 u7) u3} 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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_cone_equiv_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_descₓ'. -/
 @[simp]
 theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G ≌ Cone F)
@@ -372,7 +372,7 @@ theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
 lean 3 declaration is
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 but is expected to have type
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u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h)) s) c (CategoryTheory.Limits.IsLimit.liftConeMorphism.{u2, u4, u6, u8} K _inst_2 D _inst_4 G c P (Prefunctor.obj.{succ u3, succ u4, max (max u5 u7) u3, max (max u6 u8) u4} (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.CategoryStruct.toQuiver.{u3, max (max u5 u7) u3} (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Category.toCategoryStruct.{u3, max (max u5 u7) u3} (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F))) (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.CategoryStruct.toQuiver.{u4, max (max u6 u8) u4} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) 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+  forall {J : Type.{u5}} [_inst_1 : CategoryTheory.Category.{u1, u5} J] {K : Type.{u6}} [_inst_2 : CategoryTheory.Category.{u2, u6} K] {C : Type.{u7}} [_inst_3 : CategoryTheory.Category.{u3, u7} C] {F : CategoryTheory.Functor.{u1, u3, u5, u7} J _inst_1 C _inst_3} {D : Type.{u8}} [_inst_4 : CategoryTheory.Category.{u4, u8} D] {G : CategoryTheory.Functor.{u2, u4, u6, u8} K _inst_2 D _inst_4} (h : CategoryTheory.Equivalence.{u4, u3, max (max u8 u6) u4, max (max u7 u5) u3} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F)) {c : CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G} (P : CategoryTheory.Limits.IsLimit.{u2, u4, u6, u8} K _inst_2 D _inst_4 G c) (s : CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F), Eq.{succ u3} 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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_cone_equiv_symm_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_descₓ'. -/
 @[simp]
 theorem ofConeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
@@ -1114,7 +1114,7 @@ def ofCoconeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cocone
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_cocone_equiv_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_descₓ'. -/
 @[simp]
 theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
@@ -1129,7 +1129,7 @@ theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤
 lean 3 declaration is
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_inst_3 F) (CategoryTheory.Functor.comp.{u3, u4, u3, max u5 u7 u3, max u6 u8 u4, max u5 u7 u3} (CategoryTheory.Limits.Cocone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Equivalence.inverse.{u4, u3, max u6 u8 u4, max u5 u7 u3} (CategoryTheory.Limits.Cocone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h) (CategoryTheory.Equivalence.functor.{u4, u3, max u6 u8 u4, max u5 u7 u3} 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 but is expected to have type
-  forall {J : Type.{u5}} [_inst_1 : CategoryTheory.Category.{u1, u5} J] {K : Type.{u6}} [_inst_2 : CategoryTheory.Category.{u2, u6} K] {C : Type.{u7}} [_inst_3 : CategoryTheory.Category.{u3, u7} C] {F : CategoryTheory.Functor.{u1, u3, u5, u7} J _inst_1 C _inst_3} {D : Type.{u8}} [_inst_4 : CategoryTheory.Category.{u4, u8} D] {G : CategoryTheory.Functor.{u2, u4, u6, u8} K _inst_2 D _inst_4} (h : CategoryTheory.Equivalence.{u4, u3, max (max u8 u6) u4, max (max u7 u5) u3} (CategoryTheory.Limits.Cocone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F)) {c : CategoryTheory.Limits.Cocone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G} (P : CategoryTheory.Limits.IsColimit.{u2, u4, u6, u8} K _inst_2 D _inst_4 G c) (s : CategoryTheory.Limits.Cocone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F), Eq.{succ u3} (Quiver.Hom.{succ u3, u7} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u7} C (CategoryTheory.Category.toCategoryStruct.{u3, u7} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u3, u5, u7} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u4, succ u3, max (max u6 u8) u4, max (max u5 u7) u3} (CategoryTheory.Limits.Cocone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.CategoryStruct.toQuiver.{u4, max (max u6 u8) u4} (CategoryTheory.Limits.Cocone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Category.toCategoryStruct.{u4, max (max u6 u8) u4} (CategoryTheory.Limits.Cocone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G))) (CategoryTheory.Limits.Cocone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.CategoryStruct.toQuiver.{u3, max (max u5 u7) u3} (CategoryTheory.Limits.Cocone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Category.toCategoryStruct.{u3, max (max u5 u7) u3} 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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_cocone_equiv_symm_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_descₓ'. -/
 @[simp]
 theorem ofCoconeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -612,7 +612,7 @@ def homIso' (h : IsLimit t) (W : C) :
       { p : ∀ j, W ⟶ F.obj j // ∀ {j j'} (f : j ⟶ j'), p j ≫ F.map f = p j' } :=
   h.homIso W ≪≫
     { Hom := fun π =>
-        ⟨fun j => π.app j, fun j j' f => by convert ← (π.naturality f).symm <;> apply id_comp⟩
+        ⟨fun j => π.app j, fun j j' f => by convert← (π.naturality f).symm <;> apply id_comp⟩
       inv := fun p =>
         { app := fun j => p.1 j
           naturality' := fun j j' f => by dsimp; rw [id_comp]; exact (p.2 f).symm } }
@@ -635,7 +635,7 @@ def ofFaithful {t : Cone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [F
     uniq := fun s m w => by
       apply G.map_injective; rw [h]
       refine' ht.uniq (G.map_cone s) _ fun j => _
-      convert ← congr_arg (fun f => G.map f) (w j)
+      convert← congr_arg (fun f => G.map f) (w j)
       apply G.map_comp }
 #align category_theory.limits.is_limit.of_faithful CategoryTheory.Limits.IsLimit.ofFaithful
 
@@ -1373,8 +1373,7 @@ def homIso' (h : IsColimit t) (W : C) :
     ULift.{u₁} (t.pt ⟶ W : Type v₃) ≅
       { p : ∀ j, F.obj j ⟶ W // ∀ {j j' : J} (f : j ⟶ j'), F.map f ≫ p j' = p j } :=
   h.homIso W ≪≫
-    { Hom := fun ι =>
-        ⟨fun j => ι.app j, fun j j' f => by convert ← ι.naturality f <;> apply comp_id⟩
+    { Hom := fun ι => ⟨fun j => ι.app j, fun j j' f => by convert← ι.naturality f <;> apply comp_id⟩
       inv := fun p =>
         { app := fun j => p.1 j
           naturality' := fun j j' f => by dsimp; rw [comp_id]; exact p.2 f } }
@@ -1397,7 +1396,7 @@ def ofFaithful {t : Cocone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D)
     uniq := fun s m w => by
       apply G.map_injective; rw [h]
       refine' ht.uniq (G.map_cocone s) _ fun j => _
-      convert ← congr_arg (fun f => G.map f) (w j)
+      convert← congr_arg (fun f => G.map f) (w j)
       apply G.map_comp }
 #align category_theory.limits.is_colimit.of_faithful CategoryTheory.Limits.IsColimit.ofFaithful
 

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

@@ -357,7 +357,7 @@ def ofConeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G 
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_cone_equiv_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_descₓ'. -/
 @[simp]
 theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G ≌ Cone F)
@@ -372,7 +372,7 @@ theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
 lean 3 declaration is
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 but is expected to have type
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_inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F))) (CategoryTheory.Functor.toPrefunctor.{u4, u3, max (max u6 u8) u4, max (max u5 u7) u3} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Equivalence.functor.{u4, u3, max (max u6 u8) u4, max (max u5 u7) u3} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h)) c) (Prefunctor.map.{succ u4, succ u3, max (max u6 u8) u4, max (max u5 u7) u3} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) 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_inst_3 F))) (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.CategoryStruct.toQuiver.{u4, max (max u6 u8) u4} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Category.toCategoryStruct.{u4, max (max u6 u8) u4} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G))) (CategoryTheory.Functor.toPrefunctor.{u3, u4, max (max u5 u7) u3, max (max u6 u8) u4} (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Equivalence.inverse.{u4, u3, max (max u6 u8) u4, max (max u5 u7) u3} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h)) s) c (CategoryTheory.Limits.IsLimit.liftConeMorphism.{u2, u4, u6, u8} K _inst_2 D _inst_4 G c P (Prefunctor.obj.{succ u3, succ u4, max (max u5 u7) u3, max (max u6 u8) u4} (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.CategoryStruct.toQuiver.{u3, max (max u5 u7) u3} (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Category.toCategoryStruct.{u3, max (max u5 u7) u3} (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F))) (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.CategoryStruct.toQuiver.{u4, max (max u6 u8) u4} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) 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+  forall {J : Type.{u5}} [_inst_1 : CategoryTheory.Category.{u1, u5} J] {K : Type.{u6}} [_inst_2 : CategoryTheory.Category.{u2, u6} K] {C : Type.{u7}} [_inst_3 : CategoryTheory.Category.{u3, u7} C] {F : CategoryTheory.Functor.{u1, u3, u5, u7} J _inst_1 C _inst_3} {D : Type.{u8}} [_inst_4 : CategoryTheory.Category.{u4, u8} D] {G : CategoryTheory.Functor.{u2, u4, u6, u8} K _inst_2 D _inst_4} (h : CategoryTheory.Equivalence.{u4, u3, max (max u8 u6) u4, max (max u7 u5) u3} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F)) {c : CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G} (P : CategoryTheory.Limits.IsLimit.{u2, u4, u6, u8} K _inst_2 D _inst_4 G c) (s : CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F), Eq.{succ u3} 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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_cone_equiv_symm_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_descₓ'. -/
 @[simp]
 theorem ofConeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
@@ -1114,7 +1114,7 @@ def ofCoconeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cocone
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_cocone_equiv_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_descₓ'. -/
 @[simp]
 theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
@@ -1129,7 +1129,7 @@ theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤
 lean 3 declaration is
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 but is expected to have type
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(CategoryTheory.Limits.Cocone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h) s)))
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(CategoryTheory.Limits.Cocone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Functor.comp.{u3, u4, u3, max (max u5 u7) u3, max (max u6 u8) u4, max (max u5 u7) u3} (CategoryTheory.Limits.Cocone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Equivalence.inverse.{u4, u3, max (max u6 u8) u4, max (max u5 u7) u3} (CategoryTheory.Limits.Cocone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h) (CategoryTheory.Equivalence.functor.{u4, u3, max (max u6 u8) u4, max (max u5 u7) u3} (CategoryTheory.Limits.Cocone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h)) (CategoryTheory.Functor.id.{u3, max (max u5 u7) u3} (CategoryTheory.Limits.Cocone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F)) (CategoryTheory.Equivalence.counit.{u4, u3, max (max u6 u8) u4, max (max u5 u7) u3} (CategoryTheory.Limits.Cocone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cocone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h) s)))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_cocone_equiv_symm_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_descₓ'. -/
 @[simp]
 theorem ofCoconeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}

mathlib commit https://github.com/leanprover-community/mathlib/commit/3b267e70a936eebb21ab546f49a8df34dd300b25

@@ -622,7 +622,7 @@ def homIso' (h : IsLimit t) (W : C) :
 lean 3 declaration is
   forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {C : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} C] {F : CategoryTheory.Functor.{u1, u2, u4, u5} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F} {D : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} D] (G : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4) [_inst_5 : CategoryTheory.Faithful.{u2, u3, u5, u6} C _inst_3 D _inst_4 G] (ht : CategoryTheory.Limits.IsLimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t)) (lift : forall (s : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u5} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)), (forall (s : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Eq.{succ u3} (Quiver.Hom.{succ u3, u6} D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.obj.{u2, u3, u5, u6} C _inst_3 D _inst_4 G (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s)) (CategoryTheory.Functor.obj.{u2, u3, u5, u6} C _inst_3 D _inst_4 G (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t))) (CategoryTheory.Functor.map.{u2, u3, u5, u6} C _inst_3 D _inst_4 G (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (lift s)) (CategoryTheory.Limits.IsLimit.lift.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t) ht (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G s))) -> (CategoryTheory.Limits.IsLimit.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)
 but is expected to have type
-  forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {C : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} C] {F : CategoryTheory.Functor.{u1, u2, u4, u5} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F} {D : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} D] (G : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4) [_inst_5 : CategoryTheory.Faithful.{u2, u3, u5, u6} C _inst_3 D _inst_4 G] (ht : CategoryTheory.Limits.IsLimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t)) (lift : forall (s : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u5} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)), (forall (s : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Eq.{succ u3} (Quiver.Hom.{succ u3, u6} D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (Prefunctor.obj.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s)) (Prefunctor.obj.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t))) (Prefunctor.map.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (lift s)) (CategoryTheory.Limits.IsLimit.lift.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t) ht (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G s))) -> (CategoryTheory.Limits.IsLimit.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)
+  forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {C : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} C] {F : CategoryTheory.Functor.{u1, u2, u4, u5} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F} {D : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} D] (G : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4) [_inst_5 : CategoryTheory.Faithful.{u2, u3, u5, u6} C _inst_3 D _inst_4 G] (ht : CategoryTheory.Limits.IsLimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 G F t)) (lift : forall (s : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u5} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)), (forall (s : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Eq.{succ u3} (Quiver.Hom.{succ u3, u6} D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (Prefunctor.obj.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s)) (Prefunctor.obj.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t))) (Prefunctor.map.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (lift s)) (CategoryTheory.Limits.IsLimit.lift.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 G F t) ht (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 G F s))) -> (CategoryTheory.Limits.IsLimit.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_faithful CategoryTheory.Limits.IsLimit.ofFaithfulₓ'. -/
 /-- If G : C → D is a faithful functor which sends t to a limit cone,
   then it suffices to check that the induced maps for the image of t
@@ -639,7 +639,12 @@ def ofFaithful {t : Cone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [F
       apply G.map_comp }
 #align category_theory.limits.is_limit.of_faithful CategoryTheory.Limits.IsLimit.ofFaithful
 
-#print CategoryTheory.Limits.IsLimit.mapConeEquiv /-
+/- warning: category_theory.limits.is_limit.map_cone_equiv -> CategoryTheory.Limits.IsLimit.mapConeEquiv is a dubious translation:
+lean 3 declaration is
+  forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {C : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} C] {D : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} D] {K : CategoryTheory.Functor.{u1, u2, u4, u5} J _inst_1 C _inst_3} {F : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4} {G : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4}, (CategoryTheory.Iso.{max u5 u3, max u2 u3 u5 u6} (CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4) (CategoryTheory.Functor.category.{u2, u3, u5, u6} C _inst_3 D _inst_4) F G) -> (forall {c : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 K}, (CategoryTheory.Limits.IsLimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 K F) (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 K F c)) -> (CategoryTheory.Limits.IsLimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 K G) (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 K G c)))
+but is expected to have type
+  forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {C : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} C] {D : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} D] {K : CategoryTheory.Functor.{u1, u2, u4, u5} J _inst_1 C _inst_3} {F : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4} {G : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4}, (CategoryTheory.Iso.{max u5 u3, max (max (max u5 u6) u2) u3} (CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4) (CategoryTheory.Functor.category.{u2, u3, u5, u6} C _inst_3 D _inst_4) F G) -> (forall {c : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 K}, (CategoryTheory.Limits.IsLimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 K F) (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F K c)) -> (CategoryTheory.Limits.IsLimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 K G) (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 G K c)))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.map_cone_equiv CategoryTheory.Limits.IsLimit.mapConeEquivₓ'. -/
 /-- If `F` and `G` are naturally isomorphic, then `F.map_cone c` being a limit implies
 `G.map_cone c` is also a limit.
 -/
@@ -649,7 +654,6 @@ def mapConeEquiv {D : Type u₄} [Category.{v₄} D] {K : J ⥤ C} {F G : C ⥤
   apply postcompose_inv_equiv (iso_whisker_left K h : _) (G.map_cone c) _
   apply t.of_iso_limit (postcompose_whisker_left_map_cone h.symm c).symm
 #align category_theory.limits.is_limit.map_cone_equiv CategoryTheory.Limits.IsLimit.mapConeEquiv
--/
 
 #print CategoryTheory.Limits.IsLimit.isoUniqueConeMorphism /-
 /-- A cone is a limit cone exactly if
@@ -1380,7 +1384,7 @@ def homIso' (h : IsColimit t) (W : C) :
 lean 3 declaration is
   forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {C : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} C] {F : CategoryTheory.Functor.{u1, u2, u4, u5} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F} {D : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} D] (G : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4) [_inst_5 : CategoryTheory.Faithful.{u2, u3, u5, u6} C _inst_3 D _inst_4 G] (ht : CategoryTheory.Limits.IsColimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t)) (desc : forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u5} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s)), (forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Eq.{succ u3} (Quiver.Hom.{succ u3, u6} D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.obj.{u2, u3, u5, u6} C _inst_3 D _inst_4 G (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)) (CategoryTheory.Functor.obj.{u2, u3, u5, u6} C _inst_3 D _inst_4 G (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s))) (CategoryTheory.Functor.map.{u2, u3, u5, u6} C _inst_3 D _inst_4 G (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (desc s)) (CategoryTheory.Limits.IsColimit.desc.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t) ht (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G s))) -> (CategoryTheory.Limits.IsColimit.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)
 but is expected to have type
-  forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {C : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} C] {F : CategoryTheory.Functor.{u1, u2, u4, u5} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F} {D : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} D] (G : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4) [_inst_5 : CategoryTheory.Faithful.{u2, u3, u5, u6} C _inst_3 D _inst_4 G] (ht : CategoryTheory.Limits.IsColimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t)) (desc : forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u5} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s)), (forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Eq.{succ u3} (Quiver.Hom.{succ u3, u6} D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (Prefunctor.obj.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)) (Prefunctor.obj.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s))) (Prefunctor.map.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (desc s)) (CategoryTheory.Limits.IsColimit.desc.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t) ht (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G s))) -> (CategoryTheory.Limits.IsColimit.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)
+  forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {C : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} C] {F : CategoryTheory.Functor.{u1, u2, u4, u5} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F} {D : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} D] (G : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4) [_inst_5 : CategoryTheory.Faithful.{u2, u3, u5, u6} C _inst_3 D _inst_4 G] (ht : CategoryTheory.Limits.IsColimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 G F t)) (desc : forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u5} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s)), (forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Eq.{succ u3} (Quiver.Hom.{succ u3, u6} D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (Prefunctor.obj.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)) (Prefunctor.obj.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s))) (Prefunctor.map.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (desc s)) (CategoryTheory.Limits.IsColimit.desc.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 G F t) ht (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 G F s))) -> (CategoryTheory.Limits.IsColimit.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_faithful CategoryTheory.Limits.IsColimit.ofFaithfulₓ'. -/
 /-- If G : C → D is a faithful functor which sends t to a colimit cocone,
   then it suffices to check that the induced maps for the image of t
@@ -1397,7 +1401,12 @@ def ofFaithful {t : Cocone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D)
       apply G.map_comp }
 #align category_theory.limits.is_colimit.of_faithful CategoryTheory.Limits.IsColimit.ofFaithful
 
-#print CategoryTheory.Limits.IsColimit.mapCoconeEquiv /-
+/- warning: category_theory.limits.is_colimit.map_cocone_equiv -> CategoryTheory.Limits.IsColimit.mapCoconeEquiv is a dubious translation:
+lean 3 declaration is
+  forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {C : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} C] {D : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} D] {K : CategoryTheory.Functor.{u1, u2, u4, u5} J _inst_1 C _inst_3} {F : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4} {G : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4}, (CategoryTheory.Iso.{max u5 u3, max u2 u3 u5 u6} (CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4) (CategoryTheory.Functor.category.{u2, u3, u5, u6} C _inst_3 D _inst_4) F G) -> (forall {c : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 K}, (CategoryTheory.Limits.IsColimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 K F) (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 K F c)) -> (CategoryTheory.Limits.IsColimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 K G) (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 K G c)))
+but is expected to have type
+  forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {C : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} C] {D : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} D] {K : CategoryTheory.Functor.{u1, u2, u4, u5} J _inst_1 C _inst_3} {F : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4} {G : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4}, (CategoryTheory.Iso.{max u5 u3, max (max (max u5 u6) u2) u3} (CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4) (CategoryTheory.Functor.category.{u2, u3, u5, u6} C _inst_3 D _inst_4) F G) -> (forall {c : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 K}, (CategoryTheory.Limits.IsColimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 K F) (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F K c)) -> (CategoryTheory.Limits.IsColimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 K G) (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 G K c)))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.map_cocone_equiv CategoryTheory.Limits.IsColimit.mapCoconeEquivₓ'. -/
 /-- If `F` and `G` are naturally isomorphic, then `F.map_cone c` being a colimit implies
 `G.map_cone c` is also a colimit.
 -/
@@ -1407,7 +1416,6 @@ def mapCoconeEquiv {D : Type u₄} [Category.{v₄} D] {K : J ⥤ C} {F G : C 
   apply is_colimit.of_iso_colimit _ (precompose_whisker_left_map_cocone h c)
   apply (precompose_inv_equiv (iso_whisker_left K h : _) _).symm t
 #align category_theory.limits.is_colimit.map_cocone_equiv CategoryTheory.Limits.IsColimit.mapCoconeEquiv
--/
 
 #print CategoryTheory.Limits.IsColimit.isoUniqueCoconeMorphism /-
 /-- A cocone is a colimit cocone exactly if

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Mario Carneiro, Scott Morrison, Floris van Doorn
 
 ! This file was ported from Lean 3 source module category_theory.limits.is_limit
-! leanprover-community/mathlib commit 14b69e9f3c16630440a2cbd46f1ddad0d561dee7
+! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.CategoryTheory.Limits.Cones
 /-!
 # Limits and colimits
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We set up the general theory of limits and colimits in a category.
 In this introduction we only describe the setup for limits;
 it is repeated, with slightly different names, for colimits.

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -59,9 +59,9 @@ See <https://stacks.math.columbia.edu/tag/002E>.
   -/
 @[nolint has_nonempty_instance]
 structure IsLimit (t : Cone F) where
-  lift : ∀ s : Cone F, s.x ⟶ t.x
+  lift : ∀ s : Cone F, s.pt ⟶ t.pt
   fac : ∀ (s : Cone F) (j : J), lift s ≫ t.π.app j = s.π.app j := by obviously
-  uniq : ∀ (s : Cone F) (m : s.x ⟶ t.x) (w : ∀ j : J, m ≫ t.π.app j = s.π.app j), m = lift s := by
+  uniq : ∀ (s : Cone F) (m : s.pt ⟶ t.pt) (w : ∀ j : J, m ≫ t.π.app j = s.π.app j), m = lift s := by
     obviously
 #align category_theory.limits.is_limit CategoryTheory.Limits.IsLimit
 -/
@@ -83,14 +83,14 @@ instance subsingleton {t : Cone F} : Subsingleton (IsLimit t) :=
 #print CategoryTheory.Limits.IsLimit.map /-
 /-- Given a natural transformation `α : F ⟶ G`, we give a morphism from the cone point
 of any cone over `F` to the cone point of a limit cone over `G`. -/
-def map {F G : J ⥤ C} (s : Cone F) {t : Cone G} (P : IsLimit t) (α : F ⟶ G) : s.x ⟶ t.x :=
+def map {F G : J ⥤ C} (s : Cone F) {t : Cone G} (P : IsLimit t) (α : F ⟶ G) : s.pt ⟶ t.pt :=
   P.lift ((Cones.postcompose α).obj s)
 #align category_theory.limits.is_limit.map CategoryTheory.Limits.IsLimit.map
 -/
 
 /- warning: category_theory.limits.is_limit.map_π -> CategoryTheory.Limits.IsLimit.map_π is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} (c : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) {d : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G} (hd : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d) (α : Quiver.Hom.{max (succ u3) (succ u2), max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) F G) (j : J), 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(CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G α j))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.map_π CategoryTheory.Limits.IsLimit.map_πₓ'. -/
@@ -101,7 +101,7 @@ theorem map_π {F G : J ⥤ C} (c : Cone F) {d : Cone G} (hd : IsLimit d) (α :
 #align category_theory.limits.is_limit.map_π CategoryTheory.Limits.IsLimit.map_π
 
 #print CategoryTheory.Limits.IsLimit.lift_self /-
-theorem lift_self {c : Cone F} (t : IsLimit c) : t.lift c = 𝟙 c.x :=
+theorem lift_self {c : Cone F} (t : IsLimit c) : t.lift c = 𝟙 c.pt :=
   (t.uniq _ _ fun j => id_comp _).symm
 #align category_theory.limits.is_limit.lift_self CategoryTheory.Limits.IsLimit.lift_self
 -/
@@ -123,25 +123,25 @@ theorem uniq_cone_morphism {s t : Cone F} (h : IsLimit t) {f f' : s ⟶ t} : f =
 
 /- warning: category_theory.limits.is_limit.exists_unique -> CategoryTheory.Limits.IsLimit.existsUnique is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (forall (s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), ExistsUnique.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) (fun (l : Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) => forall (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) l (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j)))
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (forall (s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), ExistsUnique.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) (fun (l : Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) => forall (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) l (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j)))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.exists_unique CategoryTheory.Limits.IsLimit.existsUniqueₓ'. -/
 /-- Restating the definition of a limit cone in terms of the ∃! operator. -/
 theorem existsUnique {t : Cone F} (h : IsLimit t) (s : Cone F) :
-    ∃! l : s.x ⟶ t.x, ∀ j, l ≫ t.π.app j = s.π.app j :=
+    ∃! l : s.pt ⟶ t.pt, ∀ j, l ≫ t.π.app j = s.π.app j :=
   ⟨h.lift s, h.fac s, h.uniq s⟩
 #align category_theory.limits.is_limit.exists_unique CategoryTheory.Limits.IsLimit.existsUnique
 
 /- warning: category_theory.limits.is_limit.of_exists_unique -> CategoryTheory.Limits.IsLimit.ofExistsUnique is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (forall (s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), ExistsUnique.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) (fun (l : Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) => forall (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) l (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j))) -> (CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_exists_unique CategoryTheory.Limits.IsLimit.ofExistsUniqueₓ'. -/
 /-- Noncomputably make a colimit cocone from the existence of unique factorizations. -/
 def ofExistsUnique {t : Cone F}
-    (ht : ∀ s : Cone F, ∃! l : s.x ⟶ t.x, ∀ j, l ≫ t.π.app j = s.π.app j) : IsLimit t :=
+    (ht : ∀ s : Cone F, ∃! l : s.pt ⟶ t.pt, ∀ j, l ≫ t.π.app j = s.π.app j) : IsLimit t :=
   by
   choose s hs hs' using ht
   exact ⟨s, hs, hs'⟩
@@ -184,14 +184,14 @@ theorem hom_isIso {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) (f : s ⟶ t) :
 
 #print CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso /-
 /-- Limits of `F` are unique up to isomorphism. -/
-def conePointUniqueUpToIso {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) : s.x ≅ t.x :=
+def conePointUniqueUpToIso {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) : s.pt ≅ t.pt :=
   (Cones.forget F).mapIso (uniqueUpToIso P Q)
 #align category_theory.limits.is_limit.cone_point_unique_up_to_iso CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso
 -/
 
 /- warning: category_theory.limits.is_limit.cone_point_unique_up_to_iso_hom_comp -> CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (P : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (CategoryTheory.Iso.hom.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s t P Q)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_point_unique_up_to_iso_hom_comp CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_compₓ'. -/
@@ -203,7 +203,7 @@ theorem conePointUniqueUpToIso_hom_comp {s t : Cone F} (P : IsLimit s) (Q : IsLi
 
 /- warning: category_theory.limits.is_limit.cone_point_unique_up_to_iso_inv_comp -> CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp is a dubious translation:
 lean 3 declaration is
-  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (P : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Iso.inv.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s t P Q)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j)
+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (P : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Iso.inv.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s t P Q)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j)
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (P : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (CategoryTheory.Iso.inv.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s t P Q)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_point_unique_up_to_iso_inv_comp CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_compₓ'. -/
@@ -290,30 +290,31 @@ variable {t : Cone F}
 
 /- warning: category_theory.limits.is_limit.hom_lift -> CategoryTheory.Limits.IsLimit.hom_lift is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.hom_lift CategoryTheory.Limits.IsLimit.hom_liftₓ'. -/
-theorem hom_lift (h : IsLimit t) {W : C} (m : W ⟶ t.x) :
+theorem hom_lift (h : IsLimit t) {W : C} (m : W ⟶ t.pt) :
     m =
       h.lift
-        { x := W
+        { pt := W
           π := { app := fun b => m ≫ t.π.app b } } :=
   h.uniq
-    { x := W
+    { pt := W
       π := { app := fun b => m ≫ t.π.app b } } m fun b => rfl
 #align category_theory.limits.is_limit.hom_lift CategoryTheory.Limits.IsLimit.hom_lift
 
 /- warning: category_theory.limits.is_limit.hom_ext -> CategoryTheory.Limits.IsLimit.hom_ext is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (forall {W : C} {f : Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)} {f' : Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)}, (forall (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) f (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) f' (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j))) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) f f'))
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (forall {W : C} {f : Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)} {f' : Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)}, (forall (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) f (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) f' (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j))) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) f f'))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.hom_ext CategoryTheory.Limits.IsLimit.hom_extₓ'. -/
 /-- Two morphisms into a limit are equal if their compositions with
   each cone morphism are equal. -/
-theorem hom_ext (h : IsLimit t) {W : C} {f f' : W ⟶ t.x} (w : ∀ j, f ≫ t.π.app j = f' ≫ t.π.app j) :
-    f = f' := by rw [h.hom_lift f, h.hom_lift f'] <;> congr <;> exact funext w
+theorem hom_ext (h : IsLimit t) {W : C} {f f' : W ⟶ t.pt}
+    (w : ∀ j, f ≫ t.π.app j = f' ≫ t.π.app j) : f = f' := by
+  rw [h.hom_lift f, h.hom_lift f'] <;> congr <;> exact funext w
 #align category_theory.limits.is_limit.hom_ext CategoryTheory.Limits.IsLimit.hom_ext
 
 /- warning: category_theory.limits.is_limit.of_right_adjoint -> CategoryTheory.Limits.IsLimit.ofRightAdjoint is a dubious translation:
@@ -351,7 +352,7 @@ def ofConeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G 
 
 /- warning: category_theory.limits.is_limit.of_cone_equiv_apply_desc -> CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc is a dubious translation:
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 but is expected to have type
   forall {J : Type.{u5}} [_inst_1 : CategoryTheory.Category.{u1, u5} J] {K : Type.{u6}} [_inst_2 : CategoryTheory.Category.{u2, u6} K] {C : Type.{u7}} [_inst_3 : CategoryTheory.Category.{u3, u7} C] {F : CategoryTheory.Functor.{u1, u3, u5, u7} J _inst_1 C _inst_3} {D : Type.{u8}} [_inst_4 : CategoryTheory.Category.{u4, u8} D] {G : CategoryTheory.Functor.{u2, u4, u6, u8} K _inst_2 D _inst_4} (h : CategoryTheory.Equivalence.{u4, u3, max (max u8 u6) u4, max (max u7 u5) u3} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F)) {c : CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G} (P : CategoryTheory.Limits.IsLimit.{u1, u3, u5, u7} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u4, succ u3, max (max u6 u8) u4, max (max u5 u7) u3} 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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_cone_equiv_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_descₓ'. -/
@@ -366,7 +367,7 @@ theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
 
 /- warning: category_theory.limits.is_limit.of_cone_equiv_symm_apply_desc -> CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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(CategoryTheory.Category.toCategoryStruct.{u4, max (max u6 u8) u4} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G))) (CategoryTheory.Functor.toPrefunctor.{u3, u4, max (max u5 u7) u3, max (max u6 u8) u4} (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Equivalence.inverse.{u4, u3, max (max u6 u8) u4, max (max u5 u7) u3} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h)) s)))))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_cone_equiv_symm_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_descₓ'. -/
@@ -426,7 +427,7 @@ are themselves isomorphic.
 -/
 @[simps]
 def conePointsIsoOfNatIso {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit s) (Q : IsLimit t)
-    (w : F ≅ G) : s.x ≅ t.x where
+    (w : F ≅ G) : s.pt ≅ t.pt where
   Hom := Q.map s w.Hom
   inv := P.map t w.inv
   hom_inv_id' := P.hom_ext (by tidy)
@@ -436,7 +437,7 @@ def conePointsIsoOfNatIso {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit
 
 /- warning: category_theory.limits.is_limit.cone_points_iso_of_nat_iso_hom_comp -> CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G} (P : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (w : CategoryTheory.Iso.{max u3 u2, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 G j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 G j) (CategoryTheory.Iso.hom.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G s t P Q w)) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t)) G (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) j)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 G j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G (CategoryTheory.Iso.hom.{max u3 u2, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G w) j))
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G} (P : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (w : CategoryTheory.Iso.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 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(CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G (CategoryTheory.Iso.hom.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G w) j))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_hom_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_compₓ'. -/
@@ -448,7 +449,7 @@ theorem conePointsIsoOfNatIso_hom_comp {F G : J ⥤ C} {s : Cone F} {t : Cone G}
 
 /- warning: category_theory.limits.is_limit.cone_points_iso_of_nat_iso_inv_comp -> CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G} (P : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (w : CategoryTheory.Iso.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 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(max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t)) G (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 G F (CategoryTheory.Iso.inv.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G w) j))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_inv_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_compₓ'. -/
@@ -519,7 +520,7 @@ def whiskerEquivalenceEquiv {s : Cone F} (e : K ≌ J) : IsLimit s ≃ IsLimit (
 
 /- warning: category_theory.limits.is_limit.cone_points_iso_of_equivalence -> CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence is a dubious translation:
 lean 3 declaration is
-  forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {K : Type.{u5}} [_inst_2 : CategoryTheory.Category.{u2, u5} K] {C : Type.{u6}} [_inst_3 : CategoryTheory.Category.{u3, u6} C] {F : CategoryTheory.Functor.{u1, u3, u4, u6} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cone.{u1, u3, u4, u6} J _inst_1 C _inst_3 F} {G : CategoryTheory.Functor.{u2, u3, u5, u6} K _inst_2 C _inst_3} {t : CategoryTheory.Limits.Cone.{u2, u3, u5, u6} K _inst_2 C _inst_3 G}, (CategoryTheory.Limits.IsLimit.{u1, u3, u4, u6} J _inst_1 C _inst_3 F s) -> (CategoryTheory.Limits.IsLimit.{u2, u3, u5, u6} K _inst_2 C _inst_3 G t) -> (forall (e : CategoryTheory.Equivalence.{u1, u2, u4, u5} J _inst_1 K _inst_2), (CategoryTheory.Iso.{max u4 u3, max u1 u3 u4 u6} (CategoryTheory.Functor.{u1, u3, u4, u6} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u3, u4, u6} J _inst_1 C _inst_3) (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 K _inst_2 C _inst_3 (CategoryTheory.Equivalence.functor.{u1, u2, u4, u5} J _inst_1 K _inst_2 e) G) F) -> (CategoryTheory.Iso.{u3, u6} C _inst_3 (CategoryTheory.Limits.Cone.x.{u1, u3, u4, u6} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.x.{u2, u3, u5, u6} K _inst_2 C _inst_3 G t)))
+  forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {K : Type.{u5}} [_inst_2 : CategoryTheory.Category.{u2, u5} K] {C : Type.{u6}} [_inst_3 : CategoryTheory.Category.{u3, u6} C] {F : CategoryTheory.Functor.{u1, u3, u4, u6} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cone.{u1, u3, u4, u6} J _inst_1 C _inst_3 F} {G : CategoryTheory.Functor.{u2, u3, u5, u6} K _inst_2 C _inst_3} {t : CategoryTheory.Limits.Cone.{u2, u3, u5, u6} K _inst_2 C _inst_3 G}, (CategoryTheory.Limits.IsLimit.{u1, u3, u4, u6} J _inst_1 C _inst_3 F s) -> (CategoryTheory.Limits.IsLimit.{u2, u3, u5, u6} K _inst_2 C _inst_3 G t) -> (forall (e : CategoryTheory.Equivalence.{u1, u2, u4, u5} J _inst_1 K _inst_2), (CategoryTheory.Iso.{max u4 u3, max u1 u3 u4 u6} (CategoryTheory.Functor.{u1, u3, u4, u6} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u3, u4, u6} J _inst_1 C _inst_3) (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 K _inst_2 C _inst_3 (CategoryTheory.Equivalence.functor.{u1, u2, u4, u5} J _inst_1 K _inst_2 e) G) F) -> (CategoryTheory.Iso.{u3, u6} C _inst_3 (CategoryTheory.Limits.Cone.pt.{u1, u3, u4, u6} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u2, u3, u5, u6} K _inst_2 C _inst_3 G t)))
 but is expected to have type
   forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {K : Type.{u5}} [_inst_2 : CategoryTheory.Category.{u2, u5} K] {C : Type.{u6}} [_inst_3 : CategoryTheory.Category.{u3, u6} C] {F : CategoryTheory.Functor.{u1, u3, u4, u6} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cone.{u1, u3, u4, u6} J _inst_1 C _inst_3 F} {G : CategoryTheory.Functor.{u2, u3, u5, u6} K _inst_2 C _inst_3} {t : CategoryTheory.Limits.Cone.{u2, u3, u5, u6} K _inst_2 C _inst_3 G}, (CategoryTheory.Limits.IsLimit.{u1, u3, u4, u6} J _inst_1 C _inst_3 F s) -> (CategoryTheory.Limits.IsLimit.{u2, u3, u5, u6} K _inst_2 C _inst_3 G t) -> (forall (e : CategoryTheory.Equivalence.{u1, u2, u4, u5} J K _inst_1 _inst_2), (CategoryTheory.Iso.{max u4 u3, max (max (max u6 u4) u3) u1} (CategoryTheory.Functor.{u1, u3, u4, u6} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u3, u4, u6} J _inst_1 C _inst_3) (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 K _inst_2 C _inst_3 (CategoryTheory.Equivalence.functor.{u1, u2, u4, u5} J K _inst_1 _inst_2 e) G) F) -> (CategoryTheory.Iso.{u3, u6} C _inst_3 (CategoryTheory.Limits.Cone.pt.{u1, u3, u4, u6} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u2, u3, u5, u6} K _inst_2 C _inst_3 G t)))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_points_iso_of_equivalence CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalenceₓ'. -/
@@ -534,7 +535,7 @@ and the functor (up to natural isomorphism).
 -/
 @[simps]
 def conePointsIsoOfEquivalence {F : J ⥤ C} {s : Cone F} {G : K ⥤ C} {t : Cone G} (P : IsLimit s)
-    (Q : IsLimit t) (e : J ≌ K) (w : e.Functor ⋙ G ≅ F) : s.x ≅ t.x :=
+    (Q : IsLimit t) (e : J ≌ K) (w : e.Functor ⋙ G ≅ F) : s.pt ≅ t.pt :=
   let w' : e.inverse ⋙ F ≅ G := (isoWhiskerLeft e.inverse w).symm ≪≫ invFunIdAssoc e G
   { Hom := Q.lift ((Cones.equivalenceOfReindexing e.symm w').Functor.obj s)
     inv := P.lift ((Cones.equivalenceOfReindexing e w).Functor.obj t)
@@ -554,49 +555,49 @@ end Equivalence
 
 /- warning: category_theory.limits.is_limit.hom_iso -> CategoryTheory.Limits.IsLimit.homIso is a dubious translation:
 lean 3 declaration is
-  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (forall (W : C), CategoryTheory.Iso.{max u2 u3, succ (max u2 u3)} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))) (Quiver.Hom.{succ (max u2 u3), max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) W) F))
+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (forall (W : C), CategoryTheory.Iso.{max u2 u3, succ (max u2 u3)} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))) (Quiver.Hom.{succ (max u2 u3), max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) W) F))
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (forall (W : C), CategoryTheory.Iso.{max u3 u2, max (succ u3) (succ u2)} Type.{max u2 u3} CategoryTheory.types.{max u3 u2} (ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))) (Quiver.Hom.{max (succ u3) (succ u2), max (max (max u3 u1) u2) u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) W) F))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.hom_iso CategoryTheory.Limits.IsLimit.homIsoₓ'. -/
 /-- The universal property of a limit cone: a map `W ⟶ X` is the same as
   a cone on `F` with vertex `W`. -/
-def homIso (h : IsLimit t) (W : C) : ULift.{u₁} (W ⟶ t.x : Type v₃) ≅ (const J).obj W ⟶ F
+def homIso (h : IsLimit t) (W : C) : ULift.{u₁} (W ⟶ t.pt : Type v₃) ≅ (const J).obj W ⟶ F
     where
   Hom f := (t.extend f.down).π
   inv π :=
     ⟨h.lift
-        { x := W
+        { pt := W
           π }⟩
   hom_inv_id' := by ext f <;> apply h.hom_ext <;> intro j <;> simp <;> dsimp <;> rfl
 #align category_theory.limits.is_limit.hom_iso CategoryTheory.Limits.IsLimit.homIso
 
 /- warning: category_theory.limits.is_limit.hom_iso_hom -> CategoryTheory.Limits.IsLimit.homIso_hom is a dubious translation:
 lean 3 declaration is
-  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (h : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) {W : C} (f : ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))), Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) W) F) (CategoryTheory.Iso.hom.{max u2 u3, succ (max u2 u3)} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))) (Quiver.Hom.{succ (max u2 u3), max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) W) F) (CategoryTheory.Limits.IsLimit.homIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t h W) f) (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.Cone.extend.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t W (ULift.down.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) f)))
+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (h : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) {W : C} (f : ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))), Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) W) F) (CategoryTheory.Iso.hom.{max u2 u3, succ (max u2 u3)} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))) (Quiver.Hom.{succ (max u2 u3), max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) W) F) (CategoryTheory.Limits.IsLimit.homIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t h W) f) (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.Cone.extend.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t W (ULift.down.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) f)))
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (h : CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) {W : C} (f : ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max (max (max u3 u1) u2) u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) W) F) (CategoryTheory.Iso.hom.{max u3 u2, max (succ u3) (succ u2)} Type.{max u2 u3} CategoryTheory.types.{max u3 u2} (ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))) (Quiver.Hom.{max (succ u3) (succ u2), max (max (max u3 u1) u2) u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) W) F) (CategoryTheory.Limits.IsLimit.homIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t h W) f) (CategoryTheory.Limits.Cone.π.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.Cone.extend.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t W (ULift.down.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) f)))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.hom_iso_hom CategoryTheory.Limits.IsLimit.homIso_homₓ'. -/
 @[simp]
-theorem homIso_hom (h : IsLimit t) {W : C} (f : ULift.{u₁} (W ⟶ t.x)) :
+theorem homIso_hom (h : IsLimit t) {W : C} (f : ULift.{u₁} (W ⟶ t.pt)) :
     (IsLimit.homIso h W).Hom f = (t.extend f.down).π :=
   rfl
 #align category_theory.limits.is_limit.hom_iso_hom CategoryTheory.Limits.IsLimit.homIso_hom
 
 /- warning: category_theory.limits.is_limit.nat_iso -> CategoryTheory.Limits.IsLimit.natIso is a dubious translation:
 lean 3 declaration is
-  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F))
+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F))
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (CategoryTheory.Iso.{max (max u3 u4) u2, max (max (max (max (succ u3) (succ u2)) u4) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u4, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u3 u2, u4, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u3 u2, u4, succ u2, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Prefunctor.obj.{succ u2, max (succ u2) (succ u4), u4, max (succ u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}))) (CategoryTheory.Functor.toPrefunctor.{u2, max u4 u2, u4, max u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.nat_iso CategoryTheory.Limits.IsLimit.natIsoₓ'. -/
 /-- The limit of `F` represents the functor taking `W` to
   the set of cones on `F` with vertex `W`. -/
-def natIso (h : IsLimit t) : yoneda.obj t.x ⋙ uliftFunctor.{u₁} ≅ F.cones :=
+def natIso (h : IsLimit t) : yoneda.obj t.pt ⋙ uliftFunctor.{u₁} ≅ F.cones :=
   NatIso.ofComponents (fun W => IsLimit.homIso h (unop W)) (by tidy)
 #align category_theory.limits.is_limit.nat_iso CategoryTheory.Limits.IsLimit.natIso
 
 /- warning: category_theory.limits.is_limit.hom_iso' -> CategoryTheory.Limits.IsLimit.homIso' is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (forall (W : C), CategoryTheory.Iso.{max u2 u3, succ (max u2 u3)} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))) (Subtype.{max (succ u3) (succ u2)} (forall (j : J), Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j)) (fun (p : forall (j : J), Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j)) => forall {j : J} {j' : J} (f : Quiver.Hom.{succ u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) j j'), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) W (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j')) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) W (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j') (p j) (CategoryTheory.Functor.map.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j j' f)) (p j'))))
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.hom_iso' CategoryTheory.Limits.IsLimit.homIso'ₓ'. -/
@@ -604,7 +605,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.limits
 See also `hom_iso`.
 -/
 def homIso' (h : IsLimit t) (W : C) :
-    ULift.{u₁} (W ⟶ t.x : Type v₃) ≅
+    ULift.{u₁} (W ⟶ t.pt : Type v₃) ≅
       { p : ∀ j, W ⟶ F.obj j // ∀ {j j'} (f : j ⟶ j'), p j ≫ F.map f = p j' } :=
   h.homIso W ≪≫
     { Hom := fun π =>
@@ -616,7 +617,7 @@ def homIso' (h : IsLimit t) (W : C) :
 
 /- warning: category_theory.limits.is_limit.of_faithful -> CategoryTheory.Limits.IsLimit.ofFaithful is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {C : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} C] {F : CategoryTheory.Functor.{u1, u2, u4, u5} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F} {D : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} D] (G : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4) [_inst_5 : CategoryTheory.Faithful.{u2, u3, u5, u6} C _inst_3 D _inst_4 G] (ht : CategoryTheory.Limits.IsLimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t)) (lift : forall (s : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u5} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)), (forall (s : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Eq.{succ u3} (Quiver.Hom.{succ u3, u6} D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.obj.{u2, u3, u5, u6} C _inst_3 D _inst_4 G (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s)) (CategoryTheory.Functor.obj.{u2, u3, u5, u6} C _inst_3 D _inst_4 G (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t))) (CategoryTheory.Functor.map.{u2, u3, u5, u6} C _inst_3 D _inst_4 G (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (lift s)) (CategoryTheory.Limits.IsLimit.lift.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t) ht (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G s))) -> (CategoryTheory.Limits.IsLimit.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)
 but is expected to have type
   forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {C : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} C] {F : CategoryTheory.Functor.{u1, u2, u4, u5} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F} {D : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} D] (G : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4) [_inst_5 : CategoryTheory.Faithful.{u2, u3, u5, u6} C _inst_3 D _inst_4 G] (ht : CategoryTheory.Limits.IsLimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t)) (lift : forall (s : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u5} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)), (forall (s : CategoryTheory.Limits.Cone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Eq.{succ u3} (Quiver.Hom.{succ u3, u6} D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (Prefunctor.obj.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s)) (Prefunctor.obj.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t))) (Prefunctor.map.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (lift s)) (CategoryTheory.Limits.IsLimit.lift.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t) ht (CategoryTheory.Functor.mapCone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G s))) -> (CategoryTheory.Limits.IsLimit.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_faithful CategoryTheory.Limits.IsLimit.ofFaithfulₓ'. -/
@@ -624,7 +625,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.limits
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/
 def ofFaithful {t : Cone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [Faithful G]
-    (ht : IsLimit (G.mapCone t)) (lift : ∀ s : Cone F, s.x ⟶ t.x)
+    (ht : IsLimit (G.mapCone t)) (lift : ∀ s : Cone F, s.pt ⟶ t.pt)
     (h : ∀ s, G.map (lift s) = ht.lift (G.mapCone s)) : IsLimit t :=
   { lift
     fac := fun s j => by apply G.map_injective <;> rw [G.map_comp, h] <;> apply ht.fac
@@ -675,24 +676,24 @@ Case conversion may be inaccurate. Consider using '#align category_theory.limits
 /-- If `F.cones` is represented by `X`, each morphism `f : Y ⟶ X` gives a cone with cone point
 `Y`. -/
 def coneOfHom {Y : C} (f : Y ⟶ X) : Cone F where
-  x := Y
+  pt := Y
   π := h.Hom.app (op Y) ⟨f⟩
 #align category_theory.limits.is_limit.of_nat_iso.cone_of_hom CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom
 
 /- warning: category_theory.limits.is_limit.of_nat_iso.hom_of_cone -> CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone is a dubious translation:
 lean 3 declaration is
-  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C}, (CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3) X) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) -> (forall (s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) X)
+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C}, (CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3) X) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) -> (forall (s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) X)
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C}, (CategoryTheory.Iso.{max (max u3 u4) u2, max (max (max (max (succ u3) (succ u2)) u4) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u4, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u3 u2, u4, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u3 u2, u4, succ u2, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Prefunctor.obj.{succ u2, max (succ u2) (succ u4), u4, max (succ u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}))) (CategoryTheory.Functor.toPrefunctor.{u2, max u4 u2, u4, max u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3)) X) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) -> (forall (s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) X)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_nat_iso.hom_of_cone CategoryTheory.Limits.IsLimit.OfNatIso.homOfConeₓ'. -/
 /-- If `F.cones` is represented by `X`, each cone `s` gives a morphism `s.X ⟶ X`. -/
-def homOfCone (s : Cone F) : s.x ⟶ X :=
-  (h.inv.app (op s.x) s.π).down
+def homOfCone (s : Cone F) : s.pt ⟶ X :=
+  (h.inv.app (op s.pt) s.π).down
 #align category_theory.limits.is_limit.of_nat_iso.hom_of_cone CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone
 
 /- warning: category_theory.limits.is_limit.of_nat_iso.cone_of_hom_of_cone -> CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_homOfCone is a dubious translation:
 lean 3 declaration is
-  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3) X) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) (s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Eq.{max (succ u3) (succ u4) (succ u2)} (CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h s)) s
+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3) X) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) (s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Eq.{max (succ u3) (succ u4) (succ u2)} (CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h s)) s
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max (max u3 u4) u2, max (max (max (max (succ u3) (succ u2)) u4) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u4, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u3 u2, u4, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u3 u2, u4, succ u2, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Prefunctor.obj.{succ u2, max (succ u2) (succ u4), u4, max (succ u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}))) (CategoryTheory.Functor.toPrefunctor.{u2, max u4 u2, u4, max u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3)) X) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) (s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Eq.{max (max (succ u3) (succ u4)) (succ u2)} (CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h s)) s
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_nat_iso.cone_of_hom_of_cone CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_homOfConeₓ'. -/
@@ -706,7 +707,7 @@ theorem coneOfHom_homOfCone (s : Cone F) : coneOfHom h (homOfCone h s) = s :=
 
 /- warning: category_theory.limits.is_limit.of_nat_iso.hom_of_cone_of_hom -> CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone_coneOfHom is a dubious translation:
 lean 3 declaration is
-  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3) X) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) {Y : C} (f : Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) Y X), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h Y f)) X) (CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h (CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h Y f)) f
+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3) X) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) {Y : C} (f : Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) Y X), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h Y f)) X) (CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h (CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h Y f)) f
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max (max u3 u4) u2, max (max (max (max (succ u3) (succ u2)) u4) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u4, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u3 u2, u4, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u3 u2, u4, succ u2, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Prefunctor.obj.{succ u2, max (succ u2) (succ u4), u4, max (succ u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}))) (CategoryTheory.Functor.toPrefunctor.{u2, max u4 u2, u4, max u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3)) X) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) {Y : C} (f : Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) Y X), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h Y f)) X) (CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h (CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h Y f)) f
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_nat_iso.hom_of_cone_of_hom CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone_coneOfHomₓ'. -/
@@ -748,7 +749,7 @@ theorem coneOfHom_fac {Y : C} (f : Y ⟶ X) : coneOfHom h f = (limitCone h).exte
 
 /- warning: category_theory.limits.is_limit.of_nat_iso.cone_fac -> CategoryTheory.Limits.IsLimit.OfNatIso.cone_fac is a dubious translation:
 lean 3 declaration is
-  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3) X) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) (s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Eq.{max (succ u3) (succ u4) (succ u2)} (CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.extend.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.IsLimit.OfNatIso.limitCone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h) (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.Cone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.IsLimit.OfNatIso.limitCone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h)) h s)) s
+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3) X) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) (s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Eq.{max (succ u3) (succ u4) (succ u2)} (CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.extend.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.IsLimit.OfNatIso.limitCone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.IsLimit.OfNatIso.limitCone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h)) h s)) s
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max (max u3 u4) u2, max (max (max (max (succ u3) (succ u2)) u4) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u4, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u3 u2, u4, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u3 u2, u4, succ u2, max (succ u3) (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Prefunctor.obj.{succ u2, max (succ u2) (succ u4), u4, max (succ u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}))) (CategoryTheory.Functor.toPrefunctor.{u2, max u4 u2, u4, max u4 (succ u2)} C _inst_3 (CategoryTheory.Functor.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.yoneda.{u2, u4} C _inst_3)) X) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) (s : CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Eq.{max (max (succ u3) (succ u4)) (succ u2)} (CategoryTheory.Limits.Cone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.extend.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.IsLimit.OfNatIso.limitCone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h) (CategoryTheory.Limits.Cone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h s)) s
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_nat_iso.cone_fac CategoryTheory.Limits.IsLimit.OfNatIso.cone_facₓ'. -/
@@ -804,9 +805,10 @@ See <https://stacks.math.columbia.edu/tag/002F>.
 -/
 @[nolint has_nonempty_instance]
 structure IsColimit (t : Cocone F) where
-  desc : ∀ s : Cocone F, t.x ⟶ s.x
+  desc : ∀ s : Cocone F, t.pt ⟶ s.pt
   fac : ∀ (s : Cocone F) (j : J), t.ι.app j ≫ desc s = s.ι.app j := by obviously
-  uniq : ∀ (s : Cocone F) (m : t.x ⟶ s.x) (w : ∀ j : J, t.ι.app j ≫ m = s.ι.app j), m = desc s := by
+  uniq :
+    ∀ (s : Cocone F) (m : t.pt ⟶ s.pt) (w : ∀ j : J, t.ι.app j ≫ m = s.ι.app j), m = desc s := by
     obviously
 #align category_theory.limits.is_colimit CategoryTheory.Limits.IsColimit
 -/
@@ -828,14 +830,14 @@ instance subsingleton {t : Cocone F} : Subsingleton (IsColimit t) :=
 #print CategoryTheory.Limits.IsColimit.map /-
 /-- Given a natural transformation `α : F ⟶ G`, we give a morphism from the cocone point
 of a colimit cocone over `F` to the cocone point of any cocone over `G`. -/
-def map {F G : J ⥤ C} {s : Cocone F} (P : IsColimit s) (t : Cocone G) (α : F ⟶ G) : s.x ⟶ t.x :=
+def map {F G : J ⥤ C} {s : Cocone F} (P : IsColimit s) (t : Cocone G) (α : F ⟶ G) : s.pt ⟶ t.pt :=
   P.desc ((Cocones.precompose α).obj t)
 #align category_theory.limits.is_colimit.map CategoryTheory.Limits.IsColimit.map
 -/
 
 /- warning: category_theory.limits.is_colimit.ι_map -> CategoryTheory.Limits.IsColimit.ι_map is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {c : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (hc : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c) (d : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) (α : Quiver.Hom.{succ (max u3 u2), max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c)) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c) j) (CategoryTheory.Limits.IsColimit.map.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G c hc d α)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 G j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G α j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 G (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 G d) j))
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {c : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (hc : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F c) (d : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) (α : Quiver.Hom.{max (succ u3) (succ u2), max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) F G) (j : 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(CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 G) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ 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u2, u3, u4} J _inst_1 C _inst_3 F G α j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 G (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, 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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.ι_map CategoryTheory.Limits.IsColimit.ι_mapₓ'. -/
@@ -847,7 +849,7 @@ theorem ι_map {F G : J ⥤ C} {c : Cocone F} (hc : IsColimit c) (d : Cocone G)
 
 #print CategoryTheory.Limits.IsColimit.desc_self /-
 @[simp]
-theorem desc_self {t : Cocone F} (h : IsColimit t) : h.desc t = 𝟙 t.x :=
+theorem desc_self {t : Cocone F} (h : IsColimit t) : h.desc t = 𝟙 t.pt :=
   (h.uniq _ _ fun j => comp_id _).symm
 #align category_theory.limits.is_colimit.desc_self CategoryTheory.Limits.IsColimit.desc_self
 -/
@@ -869,25 +871,25 @@ theorem uniq_cocone_morphism {s t : Cocone F} (h : IsColimit t) {f f' : t ⟶ s}
 
 /- warning: category_theory.limits.is_colimit.exists_unique -> CategoryTheory.Limits.IsColimit.existsUnique is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), ExistsUnique.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (fun (d : Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) 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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.exists_unique CategoryTheory.Limits.IsColimit.existsUniqueₓ'. -/
 /-- Restating the definition of a colimit cocone in terms of the ∃! operator. -/
 theorem existsUnique {t : Cocone F} (h : IsColimit t) (s : Cocone F) :
-    ∃! d : t.x ⟶ s.x, ∀ j, t.ι.app j ≫ d = s.ι.app j :=
+    ∃! d : t.pt ⟶ s.pt, ∀ j, t.ι.app j ≫ d = s.ι.app j :=
   ⟨h.desc s, h.fac s, h.uniq s⟩
 #align category_theory.limits.is_colimit.exists_unique CategoryTheory.Limits.IsColimit.existsUnique
 
 /- warning: category_theory.limits.is_colimit.of_exists_unique -> CategoryTheory.Limits.IsColimit.ofExistsUnique is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), ExistsUnique.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (fun (d : Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) => forall (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j) d) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j))) -> (CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), ExistsUnique.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (fun (d : Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) => forall (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j) d) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j))) -> (CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_exists_unique CategoryTheory.Limits.IsColimit.ofExistsUniqueₓ'. -/
 /-- Noncomputably make a colimit cocone from the existence of unique factorizations. -/
 def ofExistsUnique {t : Cocone F}
-    (ht : ∀ s : Cocone F, ∃! d : t.x ⟶ s.x, ∀ j, t.ι.app j ≫ d = s.ι.app j) : IsColimit t :=
+    (ht : ∀ s : Cocone F, ∃! d : t.pt ⟶ s.pt, ∀ j, t.ι.app j ≫ d = s.ι.app j) : IsColimit t :=
   by
   choose s hs hs' using ht
   exact ⟨s, hs, hs'⟩
@@ -930,14 +932,14 @@ theorem hom_isIso {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t) (f : s 
 
 #print CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso /-
 /-- Colimits of `F` are unique up to isomorphism. -/
-def coconePointUniqueUpToIso {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t) : s.x ≅ t.x :=
+def coconePointUniqueUpToIso {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t) : s.pt ≅ t.pt :=
   (Cocones.forget F).mapIso (uniqueUpToIso P Q)
 #align category_theory.limits.is_colimit.cocone_point_unique_up_to_iso CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso
 -/
 
 /- warning: category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_hom -> CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (P : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j) (CategoryTheory.Iso.hom.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s t P Q))) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j)
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (P : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C 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(CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j) (CategoryTheory.Iso.hom.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s t P Q))) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_hom CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_homₓ'. -/
@@ -949,7 +951,7 @@ theorem comp_coconePointUniqueUpToIso_hom {s t : Cocone F} (P : IsColimit s) (Q
 
 /- warning: category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_inv -> CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (P : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) j) (CategoryTheory.Iso.inv.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s t P Q))) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j)
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (P : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C 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(CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) 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u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_inv CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_invₓ'. -/
@@ -1035,19 +1037,19 @@ variable {t : Cocone F}
 
 /- warning: category_theory.limits.is_colimit.hom_desc -> CategoryTheory.Limits.IsColimit.hom_desc is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.hom_desc CategoryTheory.Limits.IsColimit.hom_descₓ'. -/
-theorem hom_desc (h : IsColimit t) {W : C} (m : t.x ⟶ W) :
+theorem hom_desc (h : IsColimit t) {W : C} (m : t.pt ⟶ W) :
     m =
       h.desc
-        { x := W
+        { pt := W
           ι :=
             { app := fun b => t.ι.app b ≫ m
               naturality' := by intros <;> erw [← assoc, t.ι.naturality, comp_id, comp_id] } } :=
   h.uniq
-    { x := W
+    { pt := W
       ι :=
         { app := fun b => t.ι.app b ≫ m
           naturality' := _ } }
@@ -1056,13 +1058,13 @@ theorem hom_desc (h : IsColimit t) {W : C} (m : t.x ⟶ W) :
 
 /- warning: category_theory.limits.is_colimit.hom_ext -> CategoryTheory.Limits.IsColimit.hom_ext is a dubious translation:
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.hom_ext CategoryTheory.Limits.IsColimit.hom_extₓ'. -/
 /-- Two morphisms out of a colimit are equal if their compositions with
   each cocone morphism are equal. -/
-theorem hom_ext (h : IsColimit t) {W : C} {f f' : t.x ⟶ W}
+theorem hom_ext (h : IsColimit t) {W : C} {f f' : t.pt ⟶ W}
     (w : ∀ j, t.ι.app j ≫ f = t.ι.app j ≫ f') : f = f' := by
   rw [h.hom_desc f, h.hom_desc f'] <;> congr <;> exact funext w
 #align category_theory.limits.is_colimit.hom_ext CategoryTheory.Limits.IsColimit.hom_ext
@@ -1103,7 +1105,7 @@ def ofCoconeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cocone
 
 /- warning: category_theory.limits.is_colimit.of_cocone_equiv_apply_desc -> CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc is a dubious translation:
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_cocone_equiv_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_descₓ'. -/
@@ -1118,7 +1120,7 @@ theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤
 
 /- warning: category_theory.limits.is_colimit.of_cocone_equiv_symm_apply_desc -> CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_cocone_equiv_symm_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_descₓ'. -/
@@ -1178,7 +1180,7 @@ are themselves isomorphic.
 -/
 @[simps]
 def coconePointsIsoOfNatIso {F G : J ⥤ C} {s : Cocone F} {t : Cocone G} (P : IsColimit s)
-    (Q : IsColimit t) (w : F ≅ G) : s.x ≅ t.x
+    (Q : IsColimit t) (w : F ≅ G) : s.pt ≅ t.pt
     where
   Hom := P.map t w.Hom
   inv := Q.map s w.inv
@@ -1189,7 +1191,7 @@ def coconePointsIsoOfNatIso {F G : J ⥤ C} {s : Cocone F} {t : Cocone G} (P : I
 
 /- warning: category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_hom -> CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom is a dubious translation:
 lean 3 declaration is
-  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G} (P : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (w : CategoryTheory.Iso.{max u3 u2, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Limits.Cocone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) j) (CategoryTheory.Limits.Cocone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j) (CategoryTheory.Iso.hom.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cocone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cocone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G s t P Q w))) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 G j) (CategoryTheory.Limits.Cocone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G (CategoryTheory.Iso.hom.{max u3 u2, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G w) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 G (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) j))
+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G} (P : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (w : CategoryTheory.Iso.{max u3 u2, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j) (CategoryTheory.Iso.hom.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G s t P Q w))) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 G j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G (CategoryTheory.Iso.hom.{max u3 u2, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G w) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 G (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) j))
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G} (P : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (w : CategoryTheory.Iso.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J 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(max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) j))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_hom CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_homₓ'. -/
@@ -1201,7 +1203,7 @@ theorem comp_coconePointsIsoOfNatIso_hom {F G : J ⥤ C} {s : Cocone F} {t : Coc
 
 /- warning: category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_inv -> CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G} (P : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (w : CategoryTheory.Iso.{max u3 u2, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 G j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 G j) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t)) j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 G (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) j) (CategoryTheory.Iso.inv.{u2, u4} C _inst_3 (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F G s t P Q w))) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 G j) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 G F (CategoryTheory.Iso.inv.{max u3 u2, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G w) j) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) j))
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {G : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 G} (P : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (Q : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 G t) (w : CategoryTheory.Iso.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) F G) (j : J), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J 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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_inv CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_invₓ'. -/
@@ -1275,7 +1277,7 @@ def whiskerEquivalenceEquiv {s : Cocone F} (e : K ≌ J) :
 
 /- warning: category_theory.limits.is_colimit.cocone_points_iso_of_equivalence -> CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence is a dubious translation:
 lean 3 declaration is
-  forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {K : Type.{u5}} [_inst_2 : CategoryTheory.Category.{u2, u5} K] {C : Type.{u6}} [_inst_3 : CategoryTheory.Category.{u3, u6} C] {F : CategoryTheory.Functor.{u1, u3, u4, u6} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u3, u4, u6} J _inst_1 C _inst_3 F} {G : CategoryTheory.Functor.{u2, u3, u5, u6} K _inst_2 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u2, u3, u5, u6} K _inst_2 C _inst_3 G}, (CategoryTheory.Limits.IsColimit.{u1, u3, u4, u6} J _inst_1 C _inst_3 F s) -> (CategoryTheory.Limits.IsColimit.{u2, u3, u5, u6} K _inst_2 C _inst_3 G t) -> (forall (e : CategoryTheory.Equivalence.{u1, u2, u4, u5} J _inst_1 K _inst_2), (CategoryTheory.Iso.{max u4 u3, max u1 u3 u4 u6} (CategoryTheory.Functor.{u1, u3, u4, u6} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u3, u4, u6} J _inst_1 C _inst_3) (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 K _inst_2 C _inst_3 (CategoryTheory.Equivalence.functor.{u1, u2, u4, u5} J _inst_1 K _inst_2 e) G) F) -> (CategoryTheory.Iso.{u3, u6} C _inst_3 (CategoryTheory.Limits.Cocone.x.{u1, u3, u4, u6} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cocone.x.{u2, u3, u5, u6} K _inst_2 C _inst_3 G t)))
+  forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {K : Type.{u5}} [_inst_2 : CategoryTheory.Category.{u2, u5} K] {C : Type.{u6}} [_inst_3 : CategoryTheory.Category.{u3, u6} C] {F : CategoryTheory.Functor.{u1, u3, u4, u6} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u3, u4, u6} J _inst_1 C _inst_3 F} {G : CategoryTheory.Functor.{u2, u3, u5, u6} K _inst_2 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u2, u3, u5, u6} K _inst_2 C _inst_3 G}, (CategoryTheory.Limits.IsColimit.{u1, u3, u4, u6} J _inst_1 C _inst_3 F s) -> (CategoryTheory.Limits.IsColimit.{u2, u3, u5, u6} K _inst_2 C _inst_3 G t) -> (forall (e : CategoryTheory.Equivalence.{u1, u2, u4, u5} J _inst_1 K _inst_2), (CategoryTheory.Iso.{max u4 u3, max u1 u3 u4 u6} (CategoryTheory.Functor.{u1, u3, u4, u6} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u3, u4, u6} J _inst_1 C _inst_3) (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 K _inst_2 C _inst_3 (CategoryTheory.Equivalence.functor.{u1, u2, u4, u5} J _inst_1 K _inst_2 e) G) F) -> (CategoryTheory.Iso.{u3, u6} C _inst_3 (CategoryTheory.Limits.Cocone.pt.{u1, u3, u4, u6} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cocone.pt.{u2, u3, u5, u6} K _inst_2 C _inst_3 G t)))
 but is expected to have type
   forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {K : Type.{u5}} [_inst_2 : CategoryTheory.Category.{u2, u5} K] {C : Type.{u6}} [_inst_3 : CategoryTheory.Category.{u3, u6} C] {F : CategoryTheory.Functor.{u1, u3, u4, u6} J _inst_1 C _inst_3} {s : CategoryTheory.Limits.Cocone.{u1, u3, u4, u6} J _inst_1 C _inst_3 F} {G : CategoryTheory.Functor.{u2, u3, u5, u6} K _inst_2 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u2, u3, u5, u6} K _inst_2 C _inst_3 G}, (CategoryTheory.Limits.IsColimit.{u1, u3, u4, u6} J _inst_1 C _inst_3 F s) -> (CategoryTheory.Limits.IsColimit.{u2, u3, u5, u6} K _inst_2 C _inst_3 G t) -> (forall (e : CategoryTheory.Equivalence.{u1, u2, u4, u5} J K _inst_1 _inst_2), (CategoryTheory.Iso.{max u4 u3, max (max (max u6 u4) u3) u1} (CategoryTheory.Functor.{u1, u3, u4, u6} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u3, u4, u6} J _inst_1 C _inst_3) (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 K _inst_2 C _inst_3 (CategoryTheory.Equivalence.functor.{u1, u2, u4, u5} J K _inst_1 _inst_2 e) G) F) -> (CategoryTheory.Iso.{u3, u6} C _inst_3 (CategoryTheory.Limits.Cocone.pt.{u1, u3, u4, u6} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.Cocone.pt.{u2, u3, u5, u6} K _inst_2 C _inst_3 G t)))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.cocone_points_iso_of_equivalence CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalenceₓ'. -/
@@ -1290,7 +1292,7 @@ and the functor (up to natural isomorphism).
 -/
 @[simps]
 def coconePointsIsoOfEquivalence {F : J ⥤ C} {s : Cocone F} {G : K ⥤ C} {t : Cocone G}
-    (P : IsColimit s) (Q : IsColimit t) (e : J ≌ K) (w : e.Functor ⋙ G ≅ F) : s.x ≅ t.x :=
+    (P : IsColimit s) (Q : IsColimit t) (e : J ≌ K) (w : e.Functor ⋙ G ≅ F) : s.pt ≅ t.pt :=
   let w' : e.inverse ⋙ F ≅ G := (isoWhiskerLeft e.inverse w).symm ≪≫ invFunIdAssoc e G
   { Hom := P.desc ((Cocones.equivalenceOfReindexing e w).Functor.obj t)
     inv := Q.desc ((Cocones.equivalenceOfReindexing e.symm w').Functor.obj s)
@@ -1311,49 +1313,49 @@ end Equivalence
 
 /- warning: category_theory.limits.is_colimit.hom_iso -> CategoryTheory.Limits.IsColimit.homIso is a dubious translation:
 lean 3 declaration is
-  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (forall (W : C), CategoryTheory.Iso.{max u2 u3, succ (max u2 u3)} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) W)) (Quiver.Hom.{succ (max u2 u3), max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) F (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) W)))
+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (forall (W : C), CategoryTheory.Iso.{max u2 u3, succ (max u2 u3)} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) W)) (Quiver.Hom.{succ (max u2 u3), max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) F (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) W)))
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (forall (W : C), CategoryTheory.Iso.{max u3 u2, max (succ u3) (succ u2)} Type.{max u2 u3} CategoryTheory.types.{max u3 u2} (ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) W)) (Quiver.Hom.{max (succ u3) (succ u2), max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) W)))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.hom_iso CategoryTheory.Limits.IsColimit.homIsoₓ'. -/
 /-- The universal property of a colimit cocone: a map `X ⟶ W` is the same as
   a cocone on `F` with vertex `W`. -/
-def homIso (h : IsColimit t) (W : C) : ULift.{u₁} (t.x ⟶ W : Type v₃) ≅ F ⟶ (const J).obj W
+def homIso (h : IsColimit t) (W : C) : ULift.{u₁} (t.pt ⟶ W : Type v₃) ≅ F ⟶ (const J).obj W
     where
   Hom f := (t.extend f.down).ι
   inv ι :=
     ⟨h.desc
-        { x := W
+        { pt := W
           ι }⟩
   hom_inv_id' := by ext f <;> apply h.hom_ext <;> intro j <;> simp <;> dsimp <;> rfl
 #align category_theory.limits.is_colimit.hom_iso CategoryTheory.Limits.IsColimit.homIso
 
 /- warning: category_theory.limits.is_colimit.hom_iso_hom -> CategoryTheory.Limits.IsColimit.homIso_hom is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (h : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) {W : C} (f : ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) W)), Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) F (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) W)) (CategoryTheory.Iso.hom.{max u2 u3, succ (max u2 u3)} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) W)) (Quiver.Hom.{succ (max u2 u3), max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) F (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3) W)) (CategoryTheory.Limits.IsColimit.homIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t h W) f) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.Cocone.extend.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t W (ULift.down.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) W) f)))
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F} (h : CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) {W : C} (f : ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) W)), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) W)) (CategoryTheory.Iso.hom.{max u3 u2, max (succ u3) (succ u2)} Type.{max u2 u3} CategoryTheory.types.{max u3 u2} (ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) W)) (Quiver.Hom.{max (succ u3) (succ u2), max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) F (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u4, max (max (max u3 u1) u2) u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u1) u4) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u4, max (max (max u3 u1) u4) u2} C _inst_3 (CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} J _inst_1 C _inst_3) (CategoryTheory.Functor.const.{u1, u2, u3, u4} J _inst_1 C _inst_3)) W)) (CategoryTheory.Limits.IsColimit.homIso.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t h W) f) (CategoryTheory.Limits.Cocone.ι.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.Cocone.extend.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t W (ULift.down.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) W) f)))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.hom_iso_hom CategoryTheory.Limits.IsColimit.homIso_homₓ'. -/
 @[simp]
-theorem homIso_hom (h : IsColimit t) {W : C} (f : ULift (t.x ⟶ W)) :
+theorem homIso_hom (h : IsColimit t) {W : C} (f : ULift (t.pt ⟶ W)) :
     (IsColimit.homIso h W).Hom f = (t.extend f.down).ι :=
   rfl
 #align category_theory.limits.is_colimit.hom_iso_hom CategoryTheory.Limits.IsColimit.homIso_hom
 
 /- warning: category_theory.limits.is_colimit.nat_iso -> CategoryTheory.Limits.IsColimit.natIso is a dubious translation:
 lean 3 declaration is
-  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} C _inst_3 Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.coyoneda.{u2, u4} C _inst_3) (Opposite.op.{succ u4} C (CategoryTheory.Limits.Cocone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cocones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F))
+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} C _inst_3 Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.coyoneda.{u2, u4} C _inst_3) (Opposite.op.{succ u4} C (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cocones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F))
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (CategoryTheory.Iso.{max (max u3 u4) u2, max (max (max (max (succ u3) (succ u2)) u4) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u4, max (succ u3) (succ u2)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u3 u2, u4, max (succ u3) (succ u2)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u3 u2, u4, succ u2, max (succ u3) (succ u2)} C _inst_3 Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Prefunctor.obj.{succ u2, max (succ u4) (succ u2), u4, max u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Opposite.{succ u4} C) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3))) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}))) (CategoryTheory.Functor.toPrefunctor.{u2, max u4 u2, u4, max u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.coyoneda.{u2, u4} C _inst_3)) (Opposite.op.{succ u4} C (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t))) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cocones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.nat_iso CategoryTheory.Limits.IsColimit.natIsoₓ'. -/
 /-- The colimit of `F` represents the functor taking `W` to
   the set of cocones on `F` with vertex `W`. -/
-def natIso (h : IsColimit t) : coyoneda.obj (op t.x) ⋙ uliftFunctor.{u₁} ≅ F.cocones :=
+def natIso (h : IsColimit t) : coyoneda.obj (op t.pt) ⋙ uliftFunctor.{u₁} ≅ F.cocones :=
   NatIso.ofComponents (IsColimit.homIso h) (by intros <;> ext <;> dsimp <;> rw [← assoc] <;> rfl)
 #align category_theory.limits.is_colimit.nat_iso CategoryTheory.Limits.IsColimit.natIso
 
 /- warning: category_theory.limits.is_colimit.hom_iso' -> CategoryTheory.Limits.IsColimit.homIso' is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (forall (W : C), CategoryTheory.Iso.{max u2 u3, succ (max u2 u3)} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) W)) (Subtype.{max (succ u3) (succ u2)} (forall (j : J), Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) W) (fun (p : forall (j : J), Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) W) => forall {j : J} {j' : J} (f : Quiver.Hom.{succ u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) j j'), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) W) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j') W (CategoryTheory.Functor.map.{u1, u2, u3, u4} J _inst_1 C _inst_3 F j j' f) (p j')) (p j))))
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F}, (CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) -> (forall (W : C), CategoryTheory.Iso.{max u3 u2, max (succ u3) (succ u2)} Type.{max u2 u3} CategoryTheory.types.{max u3 u2} (ULift.{u3, u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F t) W)) (Subtype.{max (succ u3) (succ u2)} (forall (j : J), Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) W) (fun (p : forall (j : J), Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) W) => forall {j : J} {j' : J} (f : Quiver.Hom.{succ u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) j j'), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) W) (CategoryTheory.CategoryStruct.comp.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j') W (Prefunctor.map.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) j j' f) (p j')) (p j))))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.hom_iso' CategoryTheory.Limits.IsColimit.homIso'ₓ'. -/
@@ -1361,7 +1363,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.limits
 See also `hom_iso`.
 -/
 def homIso' (h : IsColimit t) (W : C) :
-    ULift.{u₁} (t.x ⟶ W : Type v₃) ≅
+    ULift.{u₁} (t.pt ⟶ W : Type v₃) ≅
       { p : ∀ j, F.obj j ⟶ W // ∀ {j j' : J} (f : j ⟶ j'), F.map f ≫ p j' = p j } :=
   h.homIso W ≪≫
     { Hom := fun ι =>
@@ -1373,7 +1375,7 @@ def homIso' (h : IsColimit t) (W : C) :
 
 /- warning: category_theory.limits.is_colimit.of_faithful -> CategoryTheory.Limits.IsColimit.ofFaithful is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {C : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} C] {F : CategoryTheory.Functor.{u1, u2, u4, u5} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F} {D : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} D] (G : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4) [_inst_5 : CategoryTheory.Faithful.{u2, u3, u5, u6} C _inst_3 D _inst_4 G] (ht : CategoryTheory.Limits.IsColimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t)) (desc : forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u5} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s)), (forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Eq.{succ u3} (Quiver.Hom.{succ u3, u6} D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.obj.{u2, u3, u5, u6} C _inst_3 D _inst_4 G (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)) (CategoryTheory.Functor.obj.{u2, u3, u5, u6} C _inst_3 D _inst_4 G (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s))) (CategoryTheory.Functor.map.{u2, u3, u5, u6} C _inst_3 D _inst_4 G (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (desc s)) (CategoryTheory.Limits.IsColimit.desc.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t) ht (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G s))) -> (CategoryTheory.Limits.IsColimit.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)
 but is expected to have type
   forall {J : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} J] {C : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} C] {F : CategoryTheory.Functor.{u1, u2, u4, u5} J _inst_1 C _inst_3} {t : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F} {D : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} D] (G : CategoryTheory.Functor.{u2, u3, u5, u6} C _inst_3 D _inst_4) [_inst_5 : CategoryTheory.Faithful.{u2, u3, u5, u6} C _inst_3 D _inst_4 G] (ht : CategoryTheory.Limits.IsColimit.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t)) (desc : forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u5} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s)), (forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u4, u5} J _inst_1 C _inst_3 F), Eq.{succ u3} (Quiver.Hom.{succ u3, u6} D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (Prefunctor.obj.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)) (Prefunctor.obj.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s))) (Prefunctor.map.{succ u2, succ u3, u5, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} C (CategoryTheory.Category.toCategoryStruct.{u2, u5} C _inst_3)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} D (CategoryTheory.Category.toCategoryStruct.{u3, u6} D _inst_4)) (CategoryTheory.Functor.toPrefunctor.{u2, u3, u5, u6} C _inst_3 D _inst_4 G) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u4, u5} J _inst_1 C _inst_3 F s) (desc s)) (CategoryTheory.Limits.IsColimit.desc.{u1, u3, u4, u6} J _inst_1 D _inst_4 (CategoryTheory.Functor.comp.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G) (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G t) ht (CategoryTheory.Functor.mapCocone.{u1, u2, u3, u4, u5, u6} J _inst_1 C _inst_3 D _inst_4 F G s))) -> (CategoryTheory.Limits.IsColimit.{u1, u2, u4, u5} J _inst_1 C _inst_3 F t)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_faithful CategoryTheory.Limits.IsColimit.ofFaithfulₓ'. -/
@@ -1381,7 +1383,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.limits
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/
 def ofFaithful {t : Cocone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [Faithful G]
-    (ht : IsColimit (G.mapCocone t)) (desc : ∀ s : Cocone F, t.x ⟶ s.x)
+    (ht : IsColimit (G.mapCocone t)) (desc : ∀ s : Cocone F, t.pt ⟶ s.pt)
     (h : ∀ s, G.map (desc s) = ht.desc (G.mapCocone s)) : IsColimit t :=
   { desc
     fac := fun s j => by apply G.map_injective <;> rw [G.map_comp, h] <;> apply ht.fac
@@ -1433,24 +1435,24 @@ Case conversion may be inaccurate. Consider using '#align category_theory.limits
 point `Y`. -/
 def coconeOfHom {Y : C} (f : X ⟶ Y) : Cocone F
     where
-  x := Y
+  pt := Y
   ι := h.Hom.app Y ⟨f⟩
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom
 
 /- warning: category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone -> CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C}, (CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} C _inst_3 Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.coyoneda.{u2, u4} C _inst_3) (Opposite.op.{succ u4} C X)) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cocones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) -> (forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) X (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s))
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C}, (CategoryTheory.Iso.{max (max u3 u4) u2, max (max (max (max (succ u3) (succ u2)) u4) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u4, max (succ u3) (succ u2)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u3 u2, u4, max (succ u3) (succ u2)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u3 u2, u4, succ u2, max (succ u3) (succ u2)} C _inst_3 Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Prefunctor.obj.{succ u2, max (succ u4) (succ u2), u4, max u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Opposite.{succ u4} C) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3))) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}))) (CategoryTheory.Functor.toPrefunctor.{u2, max u4 u2, u4, max u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.coyoneda.{u2, u4} C _inst_3)) (Opposite.op.{succ u4} C X)) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cocones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) -> (forall (s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) X (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone CategoryTheory.Limits.IsColimit.OfNatIso.homOfCoconeₓ'. -/
 /-- If `F.cocones` is corepresented by `X`, each cocone `s` gives a morphism `X ⟶ s.X`. -/
-def homOfCocone (s : Cocone F) : X ⟶ s.x :=
-  (h.inv.app s.x s.ι).down
+def homOfCocone (s : Cocone F) : X ⟶ s.pt :=
+  (h.inv.app s.pt s.ι).down
 #align category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone
 
 /- warning: category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_of_cocone -> CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_homOfCocone is a dubious translation:
 lean 3 declaration is
-  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} C _inst_3 Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.coyoneda.{u2, u4} C _inst_3) (Opposite.op.{succ u4} C X)) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cocones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) (s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Eq.{max (succ u3) (succ u4) (succ u2)} (CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h (CategoryTheory.Limits.Cocone.x.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h s)) s
+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} C _inst_3 Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.coyoneda.{u2, u4} C _inst_3) (Opposite.op.{succ u4} C X)) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cocones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) (s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Eq.{max (succ u3) (succ u4) (succ u2)} (CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h s)) s
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max (max u3 u4) u2, max (max (max (max (succ u3) (succ u2)) u4) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u4, max (succ u3) (succ u2)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u3 u2, u4, max (succ u3) (succ u2)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u3 u2, u4, succ u2, max (succ u3) (succ u2)} C _inst_3 Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Prefunctor.obj.{succ u2, max (succ u4) (succ u2), u4, max u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Opposite.{succ u4} C) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3))) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}))) (CategoryTheory.Functor.toPrefunctor.{u2, max u4 u2, u4, max u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.coyoneda.{u2, u4} C _inst_3)) (Opposite.op.{succ u4} C X)) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cocones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) (s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Eq.{max (max (succ u3) (succ u4)) (succ u2)} (CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h s)) s
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_of_cocone CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_homOfCoconeₓ'. -/
@@ -1464,7 +1466,7 @@ theorem coconeOfHom_homOfCocone (s : Cocone F) : coconeOfHom h (homOfCocone h s)
 
 /- warning: category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone_of_hom -> CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone_cooneOfHom is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} C _inst_3 Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.coyoneda.{u2, u4} C _inst_3) (Opposite.op.{succ u4} C X)) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cocones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) {Y : C} (f : Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) X Y), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_3)) X (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h Y f))) (CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h (CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h Y f)) f
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone_of_hom CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone_cooneOfHomₓ'. -/
@@ -1506,7 +1508,7 @@ theorem coconeOfHom_fac {Y : C} (f : X ⟶ Y) : coconeOfHom h f = (colimitCocone
 
 /- warning: category_theory.limits.is_colimit.of_nat_iso.cocone_fac -> CategoryTheory.Limits.IsColimit.OfNatIso.cocone_fac is a dubious translation:
 lean 3 declaration is
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+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} C _inst_3 Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.coyoneda.{u2, u4} C _inst_3) (Opposite.op.{succ u4} C X)) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cocones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) (s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Eq.{max (succ u3) (succ u4) (succ u2)} (CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.extend.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.IsColimit.OfNatIso.colimitCocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.IsColimit.OfNatIso.colimitCocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h)) h s)) s
 but is expected to have type
   forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max (max u3 u4) u2, max (max (max (max (succ u3) (succ u2)) u4) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u4, max (succ u3) (succ u2)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u3 u2, u4, max (succ u3) (succ u2)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u3 u2, u4, succ u2, max (succ u3) (succ u2)} C _inst_3 Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Prefunctor.obj.{succ u2, max (succ u4) (succ u2), u4, max u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Opposite.{succ u4} C) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3))) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}))) (CategoryTheory.Functor.toPrefunctor.{u2, max u4 u2, u4, max u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.coyoneda.{u2, u4} C _inst_3)) (Opposite.op.{succ u4} C X)) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cocones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)) (s : CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F), Eq.{max (max (succ u3) (succ u4)) (succ u2)} (CategoryTheory.Limits.Cocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cocone.extend.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.IsColimit.OfNatIso.colimitCocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h) (CategoryTheory.Limits.Cocone.pt.{u1, u2, u3, u4} J _inst_1 C _inst_3 F s) (CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h s)) s
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_nat_iso.cocone_fac CategoryTheory.Limits.IsColimit.OfNatIso.cocone_facₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -51,6 +51,7 @@ variable {C : Type u₃} [Category.{v₃} C]
 
 variable {F : J ⥤ C}
 
+#print CategoryTheory.Limits.IsLimit /-
 /-- A cone `t` on `F` is a limit cone if each cone on `F` admits a unique
 cone morphism to `t`.
 
@@ -59,10 +60,11 @@ See <https://stacks.math.columbia.edu/tag/002E>.
 @[nolint has_nonempty_instance]
 structure IsLimit (t : Cone F) where
   lift : ∀ s : Cone F, s.x ⟶ t.x
-  fac' : ∀ (s : Cone F) (j : J), lift s ≫ t.π.app j = s.π.app j := by obviously
-  uniq' : ∀ (s : Cone F) (m : s.x ⟶ t.x) (w : ∀ j : J, m ≫ t.π.app j = s.π.app j), m = lift s := by
+  fac : ∀ (s : Cone F) (j : J), lift s ≫ t.π.app j = s.π.app j := by obviously
+  uniq : ∀ (s : Cone F) (m : s.x ⟶ t.x) (w : ∀ j : J, m ≫ t.π.app j = s.π.app j), m = lift s := by
     obviously
 #align category_theory.limits.is_limit CategoryTheory.Limits.IsLimit
+-/
 
 restate_axiom is_limit.fac'
 
@@ -72,43 +74,71 @@ restate_axiom is_limit.uniq'
 
 namespace IsLimit
 
+#print CategoryTheory.Limits.IsLimit.subsingleton /-
 instance subsingleton {t : Cone F} : Subsingleton (IsLimit t) :=
   ⟨by intro P Q <;> cases P <;> cases Q <;> congr <;> ext <;> solve_by_elim⟩
 #align category_theory.limits.is_limit.subsingleton CategoryTheory.Limits.IsLimit.subsingleton
+-/
 
+#print CategoryTheory.Limits.IsLimit.map /-
 /-- Given a natural transformation `α : F ⟶ G`, we give a morphism from the cone point
 of any cone over `F` to the cone point of a limit cone over `G`. -/
 def map {F G : J ⥤ C} (s : Cone F) {t : Cone G} (P : IsLimit t) (α : F ⟶ G) : s.x ⟶ t.x :=
   P.lift ((Cones.postcompose α).obj s)
 #align category_theory.limits.is_limit.map CategoryTheory.Limits.IsLimit.map
+-/
 
+/- warning: category_theory.limits.is_limit.map_π -> CategoryTheory.Limits.IsLimit.map_π is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.map_π CategoryTheory.Limits.IsLimit.map_πₓ'. -/
 @[simp, reassoc.1]
 theorem map_π {F G : J ⥤ C} (c : Cone F) {d : Cone G} (hd : IsLimit d) (α : F ⟶ G) (j : J) :
     hd.map c α ≫ d.π.app j = c.π.app j ≫ α.app j :=
   fac _ _ _
 #align category_theory.limits.is_limit.map_π CategoryTheory.Limits.IsLimit.map_π
 
+#print CategoryTheory.Limits.IsLimit.lift_self /-
 theorem lift_self {c : Cone F} (t : IsLimit c) : t.lift c = 𝟙 c.x :=
   (t.uniq _ _ fun j => id_comp _).symm
 #align category_theory.limits.is_limit.lift_self CategoryTheory.Limits.IsLimit.lift_self
+-/
 
+#print CategoryTheory.Limits.IsLimit.liftConeMorphism /-
 -- Repackaging the definition in terms of cone morphisms.
 /-- The universal morphism from any other cone to a limit cone. -/
 @[simps]
 def liftConeMorphism {t : Cone F} (h : IsLimit t) (s : Cone F) : s ⟶ t where Hom := h.lift s
 #align category_theory.limits.is_limit.lift_cone_morphism CategoryTheory.Limits.IsLimit.liftConeMorphism
+-/
 
+#print CategoryTheory.Limits.IsLimit.uniq_cone_morphism /-
 theorem uniq_cone_morphism {s t : Cone F} (h : IsLimit t) {f f' : s ⟶ t} : f = f' :=
   have : ∀ {g : s ⟶ t}, g = h.liftConeMorphism s := by intro g <;> ext <;> exact h.uniq _ _ g.w
   this.trans this.symm
 #align category_theory.limits.is_limit.uniq_cone_morphism CategoryTheory.Limits.IsLimit.uniq_cone_morphism
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.exists_unique CategoryTheory.Limits.IsLimit.existsUniqueₓ'. -/
 /-- Restating the definition of a limit cone in terms of the ∃! operator. -/
 theorem existsUnique {t : Cone F} (h : IsLimit t) (s : Cone F) :
     ∃! l : s.x ⟶ t.x, ∀ j, l ≫ t.π.app j = s.π.app j :=
   ⟨h.lift s, h.fac s, h.uniq s⟩
 #align category_theory.limits.is_limit.exists_unique CategoryTheory.Limits.IsLimit.existsUnique
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_exists_unique CategoryTheory.Limits.IsLimit.ofExistsUniqueₓ'. -/
 /-- Noncomputably make a colimit cocone from the existence of unique factorizations. -/
 def ofExistsUnique {t : Cone F}
     (ht : ∀ s : Cone F, ∃! l : s.x ⟶ t.x, ∀ j, l ≫ t.π.app j = s.π.app j) : IsLimit t :=
@@ -117,6 +147,7 @@ def ofExistsUnique {t : Cone F}
   exact ⟨s, hs, hs'⟩
 #align category_theory.limits.is_limit.of_exists_unique CategoryTheory.Limits.IsLimit.ofExistsUnique
 
+#print CategoryTheory.Limits.IsLimit.mkConeMorphism /-
 /-- Alternative constructor for `is_limit`,
 providing a morphism of cones rather than a morphism between the cone points
 and separately the factorisation condition.
@@ -126,11 +157,13 @@ def mkConeMorphism {t : Cone F} (lift : ∀ s : Cone F, s ⟶ t)
     (uniq' : ∀ (s : Cone F) (m : s ⟶ t), m = lift s) : IsLimit t
     where
   lift s := (lift s).Hom
-  uniq' s m w :=
+  uniq s m w :=
     have : ConeMorphism.mk m w = lift s := by apply uniq'
     congr_arg ConeMorphism.hom this
 #align category_theory.limits.is_limit.mk_cone_morphism CategoryTheory.Limits.IsLimit.mkConeMorphism
+-/
 
+#print CategoryTheory.Limits.IsLimit.uniqueUpToIso /-
 /-- Limit cones on `F` are unique up to isomorphism. -/
 @[simps]
 def uniqueUpToIso {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) : s ≅ t
@@ -140,53 +173,79 @@ def uniqueUpToIso {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) : s ≅ t
   hom_inv_id' := P.uniq_cone_morphism
   inv_hom_id' := Q.uniq_cone_morphism
 #align category_theory.limits.is_limit.unique_up_to_iso CategoryTheory.Limits.IsLimit.uniqueUpToIso
+-/
 
+#print CategoryTheory.Limits.IsLimit.hom_isIso /-
 /-- Any cone morphism between limit cones is an isomorphism. -/
 theorem hom_isIso {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) (f : s ⟶ t) : IsIso f :=
   ⟨⟨P.liftConeMorphism t, ⟨P.uniq_cone_morphism, Q.uniq_cone_morphism⟩⟩⟩
 #align category_theory.limits.is_limit.hom_is_iso CategoryTheory.Limits.IsLimit.hom_isIso
+-/
 
+#print CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso /-
 /-- Limits of `F` are unique up to isomorphism. -/
 def conePointUniqueUpToIso {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) : s.x ≅ t.x :=
   (Cones.forget F).mapIso (uniqueUpToIso P Q)
 #align category_theory.limits.is_limit.cone_point_unique_up_to_iso CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso
+-/
 
+/- warning: category_theory.limits.is_limit.cone_point_unique_up_to_iso_hom_comp -> CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_point_unique_up_to_iso_hom_comp CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_compₓ'. -/
 @[simp, reassoc.1]
 theorem conePointUniqueUpToIso_hom_comp {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) (j : J) :
     (conePointUniqueUpToIso P Q).Hom ≫ t.π.app j = s.π.app j :=
   (uniqueUpToIso P Q).Hom.w _
 #align category_theory.limits.is_limit.cone_point_unique_up_to_iso_hom_comp CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_point_unique_up_to_iso_inv_comp CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_compₓ'. -/
 @[simp, reassoc.1]
 theorem conePointUniqueUpToIso_inv_comp {s t : Cone F} (P : IsLimit s) (Q : IsLimit t) (j : J) :
     (conePointUniqueUpToIso P Q).inv ≫ s.π.app j = t.π.app j :=
   (uniqueUpToIso P Q).inv.w _
 #align category_theory.limits.is_limit.cone_point_unique_up_to_iso_inv_comp CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp
 
+#print CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_hom /-
 @[simp, reassoc.1]
 theorem lift_comp_conePointUniqueUpToIso_hom {r s t : Cone F} (P : IsLimit s) (Q : IsLimit t) :
     P.lift r ≫ (conePointUniqueUpToIso P Q).Hom = Q.lift r :=
   Q.uniq _ _ (by simp)
 #align category_theory.limits.is_limit.lift_comp_cone_point_unique_up_to_iso_hom CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_hom
+-/
 
+#print CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_inv /-
 @[simp, reassoc.1]
 theorem lift_comp_conePointUniqueUpToIso_inv {r s t : Cone F} (P : IsLimit s) (Q : IsLimit t) :
     Q.lift r ≫ (conePointUniqueUpToIso P Q).inv = P.lift r :=
   P.uniq _ _ (by simp)
 #align category_theory.limits.is_limit.lift_comp_cone_point_unique_up_to_iso_inv CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_inv
+-/
 
+#print CategoryTheory.Limits.IsLimit.ofIsoLimit /-
 /-- Transport evidence that a cone is a limit cone across an isomorphism of cones. -/
 def ofIsoLimit {r t : Cone F} (P : IsLimit r) (i : r ≅ t) : IsLimit t :=
   IsLimit.mkConeMorphism (fun s => P.liftConeMorphism s ≫ i.Hom) fun s m => by
     rw [← i.comp_inv_eq] <;> apply P.uniq_cone_morphism
 #align category_theory.limits.is_limit.of_iso_limit CategoryTheory.Limits.IsLimit.ofIsoLimit
+-/
 
+#print CategoryTheory.Limits.IsLimit.ofIsoLimit_lift /-
 @[simp]
 theorem ofIsoLimit_lift {r t : Cone F} (P : IsLimit r) (i : r ≅ t) (s) :
     (P.ofIsoLimit i).lift s = P.lift s ≫ i.Hom.Hom :=
   rfl
 #align category_theory.limits.is_limit.of_iso_limit_lift CategoryTheory.Limits.IsLimit.ofIsoLimit_lift
+-/
 
+#print CategoryTheory.Limits.IsLimit.equivIsoLimit /-
 /-- Isomorphism of cones preserves whether or not they are limiting cones. -/
 def equivIsoLimit {r t : Cone F} (i : r ≅ t) : IsLimit r ≃ IsLimit t
     where
@@ -195,19 +254,25 @@ def equivIsoLimit {r t : Cone F} (i : r ≅ t) : IsLimit r ≃ IsLimit t
   left_inv := by tidy
   right_inv := by tidy
 #align category_theory.limits.is_limit.equiv_iso_limit CategoryTheory.Limits.IsLimit.equivIsoLimit
+-/
 
+#print CategoryTheory.Limits.IsLimit.equivIsoLimit_apply /-
 @[simp]
 theorem equivIsoLimit_apply {r t : Cone F} (i : r ≅ t) (P : IsLimit r) :
     equivIsoLimit i P = P.ofIsoLimit i :=
   rfl
 #align category_theory.limits.is_limit.equiv_iso_limit_apply CategoryTheory.Limits.IsLimit.equivIsoLimit_apply
+-/
 
+#print CategoryTheory.Limits.IsLimit.equivIsoLimit_symm_apply /-
 @[simp]
 theorem equivIsoLimit_symm_apply {r t : Cone F} (i : r ≅ t) (P : IsLimit t) :
     (equivIsoLimit i).symm P = P.ofIsoLimit i.symm :=
   rfl
 #align category_theory.limits.is_limit.equiv_iso_limit_symm_apply CategoryTheory.Limits.IsLimit.equivIsoLimit_symm_apply
+-/
 
+#print CategoryTheory.Limits.IsLimit.ofPointIso /-
 /-- If the canonical morphism from a cone point to a limiting cone point is an iso, then the
 first cone was limiting also.
 -/
@@ -219,9 +284,16 @@ def ofPointIso {r t : Cone F} (P : IsLimit r) [i : IsIso (P.lift t)] : IsLimit t
       symm
       apply as_iso (P.lift_cone_morphism t))
 #align category_theory.limits.is_limit.of_point_iso CategoryTheory.Limits.IsLimit.ofPointIso
+-/
 
 variable {t : Cone F}
 
+/- warning: category_theory.limits.is_limit.hom_lift -> CategoryTheory.Limits.IsLimit.hom_lift is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.hom_lift CategoryTheory.Limits.IsLimit.hom_liftₓ'. -/
 theorem hom_lift (h : IsLimit t) {W : C} (m : W ⟶ t.x) :
     m =
       h.lift
@@ -232,12 +304,24 @@ theorem hom_lift (h : IsLimit t) {W : C} (m : W ⟶ t.x) :
       π := { app := fun b => m ≫ t.π.app b } } m fun b => rfl
 #align category_theory.limits.is_limit.hom_lift CategoryTheory.Limits.IsLimit.hom_lift
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.hom_ext CategoryTheory.Limits.IsLimit.hom_extₓ'. -/
 /-- Two morphisms into a limit are equal if their compositions with
   each cone morphism are equal. -/
 theorem hom_ext (h : IsLimit t) {W : C} {f f' : W ⟶ t.x} (w : ∀ j, f ≫ t.π.app j = f' ≫ t.π.app j) :
     f = f' := by rw [h.hom_lift f, h.hom_lift f'] <;> congr <;> exact funext w
 #align category_theory.limits.is_limit.hom_ext CategoryTheory.Limits.IsLimit.hom_ext
 
+/- warning: category_theory.limits.is_limit.of_right_adjoint -> CategoryTheory.Limits.IsLimit.ofRightAdjoint is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_right_adjoint CategoryTheory.Limits.IsLimit.ofRightAdjointₓ'. -/
 /-- Given a right adjoint functor between categories of cones,
 the image of a limit cone is a limit cone.
 -/
@@ -247,6 +331,12 @@ def ofRightAdjoint {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G
     fun s m => (Adjunction.eq_homEquiv_apply _ _ _).2 t.uniq_cone_morphism
 #align category_theory.limits.is_limit.of_right_adjoint CategoryTheory.Limits.IsLimit.ofRightAdjoint
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_cone_equiv CategoryTheory.Limits.IsLimit.ofConeEquivₓ'. -/
 /-- Given two functors which have equivalent categories of cones, we can transport a limiting cone
 across the equivalence.
 -/
@@ -259,6 +349,12 @@ def ofConeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G 
   right_inv := by tidy
 #align category_theory.limits.is_limit.of_cone_equiv CategoryTheory.Limits.IsLimit.ofConeEquiv
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_cone_equiv_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_descₓ'. -/
 @[simp]
 theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G ≌ Cone F)
     {c : Cone G} (P : IsLimit (h.Functor.obj c)) (s) :
@@ -268,6 +364,12 @@ theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
   rfl
 #align category_theory.limits.is_limit.of_cone_equiv_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc
 
+/- warning: category_theory.limits.is_limit.of_cone_equiv_symm_apply_desc -> CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc is a dubious translation:
+lean 3 declaration is
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_inst_3 F) h) s) c (CategoryTheory.Limits.IsLimit.liftConeMorphism.{u2, u4, u6, u8} K _inst_2 D _inst_4 G c P (CategoryTheory.Functor.obj.{u3, u4, max u5 u7 u3, max u6 u8 u4} (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Equivalence.inverse.{u4, u3, max u6 u8 u4, max u5 u7 u3} (CategoryTheory.Limits.Cone.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.category.{u2, u4, u6, u8} K _inst_2 D _inst_4 G) (CategoryTheory.Limits.Cone.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) (CategoryTheory.Limits.Cone.category.{u1, u3, u5, u7} J _inst_1 C _inst_3 F) h) s)))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_cone_equiv_symm_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_descₓ'. -/
 @[simp]
 theorem ofConeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
     (h : Cone G ≌ Cone F) {c : Cone G} (P : IsLimit c) (s) :
@@ -276,6 +378,12 @@ theorem ofConeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K 
   rfl
 #align category_theory.limits.is_limit.of_cone_equiv_symm_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc
 
+/- warning: category_theory.limits.is_limit.postcompose_hom_equiv -> CategoryTheory.Limits.IsLimit.postcomposeHomEquiv is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.postcompose_hom_equiv CategoryTheory.Limits.IsLimit.postcomposeHomEquivₓ'. -/
 /--
 A cone postcomposed with a natural isomorphism is a limit cone if and only if the original cone is.
 -/
@@ -284,6 +392,12 @@ def postcomposeHomEquiv {F G : J ⥤ C} (α : F ≅ G) (c : Cone F) :
   ofConeEquiv (Cones.postcomposeEquivalence α)
 #align category_theory.limits.is_limit.postcompose_hom_equiv CategoryTheory.Limits.IsLimit.postcomposeHomEquiv
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.postcompose_inv_equiv CategoryTheory.Limits.IsLimit.postcomposeInvEquivₓ'. -/
 /-- A cone postcomposed with the inverse of a natural isomorphism is a limit cone if and only if
 the original cone is.
 -/
@@ -292,6 +406,12 @@ def postcomposeInvEquiv {F G : J ⥤ C} (α : F ≅ G) (c : Cone G) :
   postcomposeHomEquiv α.symm c
 #align category_theory.limits.is_limit.postcompose_inv_equiv CategoryTheory.Limits.IsLimit.postcomposeInvEquiv
 
+/- warning: category_theory.limits.is_limit.equiv_of_nat_iso_of_iso -> CategoryTheory.Limits.IsLimit.equivOfNatIsoOfIso is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.equiv_of_nat_iso_of_iso CategoryTheory.Limits.IsLimit.equivOfNatIsoOfIsoₓ'. -/
 /-- Constructing an equivalence `is_limit c ≃ is_limit d` from a natural isomorphism
 between the underlying functors, and then an isomorphism between `c` transported along this and `d`.
 -/
@@ -300,6 +420,7 @@ def equivOfNatIsoOfIso {F G : J ⥤ C} (α : F ≅ G) (c : Cone F) (d : Cone G)
   (postcomposeHomEquiv α _).symm.trans (equivIsoLimit w)
 #align category_theory.limits.is_limit.equiv_of_nat_iso_of_iso CategoryTheory.Limits.IsLimit.equivOfNatIsoOfIso
 
+#print CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso /-
 /-- The cone points of two limit cones for naturally isomorphic functors
 are themselves isomorphic.
 -/
@@ -311,43 +432,72 @@ def conePointsIsoOfNatIso {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit
   hom_inv_id' := P.hom_ext (by tidy)
   inv_hom_id' := Q.hom_ext (by tidy)
 #align category_theory.limits.is_limit.cone_points_iso_of_nat_iso CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_hom_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_compₓ'. -/
 @[reassoc.1]
 theorem conePointsIsoOfNatIso_hom_comp {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit s)
     (Q : IsLimit t) (w : F ≅ G) (j : J) :
     (conePointsIsoOfNatIso P Q w).Hom ≫ t.π.app j = s.π.app j ≫ w.Hom.app j := by simp
 #align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_hom_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp
 
+/- warning: category_theory.limits.is_limit.cone_points_iso_of_nat_iso_inv_comp -> CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_inv_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_compₓ'. -/
 @[reassoc.1]
 theorem conePointsIsoOfNatIso_inv_comp {F G : J ⥤ C} {s : Cone F} {t : Cone G} (P : IsLimit s)
     (Q : IsLimit t) (w : F ≅ G) (j : J) :
     (conePointsIsoOfNatIso P Q w).inv ≫ s.π.app j = t.π.app j ≫ w.inv.app j := by simp
 #align category_theory.limits.is_limit.cone_points_iso_of_nat_iso_inv_comp CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp
 
+#print CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom /-
 @[reassoc.1]
 theorem lift_comp_conePointsIsoOfNatIso_hom {F G : J ⥤ C} {r s : Cone F} {t : Cone G}
     (P : IsLimit s) (Q : IsLimit t) (w : F ≅ G) :
     P.lift r ≫ (conePointsIsoOfNatIso P Q w).Hom = Q.map r w.Hom :=
   Q.hom_ext (by simp)
 #align category_theory.limits.is_limit.lift_comp_cone_points_iso_of_nat_iso_hom CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom
+-/
 
+#print CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv /-
 @[reassoc.1]
 theorem lift_comp_conePointsIsoOfNatIso_inv {F G : J ⥤ C} {r s : Cone G} {t : Cone F}
     (P : IsLimit t) (Q : IsLimit s) (w : F ≅ G) :
     Q.lift r ≫ (conePointsIsoOfNatIso P Q w).inv = P.map r w.inv :=
   P.hom_ext (by simp)
 #align category_theory.limits.is_limit.lift_comp_cone_points_iso_of_nat_iso_inv CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv
+-/
 
 section Equivalence
 
 open CategoryTheory.Equivalence
 
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 /-- If `s : cone F` is a limit cone, so is `s` whiskered by an equivalence `e`.
 -/
 def whiskerEquivalence {s : Cone F} (P : IsLimit s) (e : K ≌ J) : IsLimit (s.whisker e.Functor) :=
   ofRightAdjoint (Cones.whiskeringEquivalence e).Functor P
 #align category_theory.limits.is_limit.whisker_equivalence CategoryTheory.Limits.IsLimit.whiskerEquivalence
 
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 /-- If `s : cone F` whiskered by an equivalence `e` is a limit cone, so is `s`.
 -/
 def ofWhiskerEquivalence {s : Cone F} (e : K ≌ J) (P : IsLimit (s.whisker e.Functor)) : IsLimit s :=
@@ -355,12 +505,24 @@ def ofWhiskerEquivalence {s : Cone F} (e : K ≌ J) (P : IsLimit (s.whisker e.Fu
     (ofRightAdjoint (Cones.whiskeringEquivalence e).inverse P : _)
 #align category_theory.limits.is_limit.of_whisker_equivalence CategoryTheory.Limits.IsLimit.ofWhiskerEquivalence
 
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 /-- Given an equivalence of diagrams `e`, `s` is a limit cone iff `s.whisker e.functor` is.
 -/
 def whiskerEquivalenceEquiv {s : Cone F} (e : K ≌ J) : IsLimit s ≃ IsLimit (s.whisker e.Functor) :=
   ⟨fun h => h.whiskerEquivalence e, ofWhiskerEquivalence e, by tidy, by tidy⟩
 #align category_theory.limits.is_limit.whisker_equivalence_equiv CategoryTheory.Limits.IsLimit.whiskerEquivalenceEquiv
 
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 /-- We can prove two cone points `(s : cone F).X` and `(t.cone G).X` are isomorphic if
 * both cones are limit cones
 * their indexing categories are equivalent via some `e : J ≌ K`,
@@ -390,6 +552,12 @@ def conePointsIsoOfEquivalence {F : J ⥤ C} {s : Cone F} {G : K ⥤ C} {t : Con
 
 end Equivalence
 
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 /-- The universal property of a limit cone: a map `W ⟶ X` is the same as
   a cone on `F` with vertex `W`. -/
 def homIso (h : IsLimit t) (W : C) : ULift.{u₁} (W ⟶ t.x : Type v₃) ≅ (const J).obj W ⟶ F
@@ -402,18 +570,36 @@ def homIso (h : IsLimit t) (W : C) : ULift.{u₁} (W ⟶ t.x : Type v₃) ≅ (c
   hom_inv_id' := by ext f <;> apply h.hom_ext <;> intro j <;> simp <;> dsimp <;> rfl
 #align category_theory.limits.is_limit.hom_iso CategoryTheory.Limits.IsLimit.homIso
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.hom_iso_hom CategoryTheory.Limits.IsLimit.homIso_homₓ'. -/
 @[simp]
 theorem homIso_hom (h : IsLimit t) {W : C} (f : ULift.{u₁} (W ⟶ t.x)) :
     (IsLimit.homIso h W).Hom f = (t.extend f.down).π :=
   rfl
 #align category_theory.limits.is_limit.hom_iso_hom CategoryTheory.Limits.IsLimit.homIso_hom
 
+/- warning: category_theory.limits.is_limit.nat_iso -> CategoryTheory.Limits.IsLimit.natIso is a dubious translation:
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 /-- The limit of `F` represents the functor taking `W` to
   the set of cones on `F` with vertex `W`. -/
 def natIso (h : IsLimit t) : yoneda.obj t.x ⋙ uliftFunctor.{u₁} ≅ F.cones :=
   NatIso.ofComponents (fun W => IsLimit.homIso h (unop W)) (by tidy)
 #align category_theory.limits.is_limit.nat_iso CategoryTheory.Limits.IsLimit.natIso
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.hom_iso' CategoryTheory.Limits.IsLimit.homIso'ₓ'. -/
 /-- Another, more explicit, formulation of the universal property of a limit cone.
 See also `hom_iso`.
 -/
@@ -428,6 +614,12 @@ def homIso' (h : IsLimit t) (W : C) :
           naturality' := fun j j' f => by dsimp; rw [id_comp]; exact (p.2 f).symm } }
 #align category_theory.limits.is_limit.hom_iso' CategoryTheory.Limits.IsLimit.homIso'
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_faithful CategoryTheory.Limits.IsLimit.ofFaithfulₓ'. -/
 /-- If G : C → D is a faithful functor which sends t to a limit cone,
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/
@@ -435,14 +627,15 @@ def ofFaithful {t : Cone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [F
     (ht : IsLimit (G.mapCone t)) (lift : ∀ s : Cone F, s.x ⟶ t.x)
     (h : ∀ s, G.map (lift s) = ht.lift (G.mapCone s)) : IsLimit t :=
   { lift
-    fac' := fun s j => by apply G.map_injective <;> rw [G.map_comp, h] <;> apply ht.fac
-    uniq' := fun s m w => by
+    fac := fun s j => by apply G.map_injective <;> rw [G.map_comp, h] <;> apply ht.fac
+    uniq := fun s m w => by
       apply G.map_injective; rw [h]
       refine' ht.uniq (G.map_cone s) _ fun j => _
       convert ← congr_arg (fun f => G.map f) (w j)
       apply G.map_comp }
 #align category_theory.limits.is_limit.of_faithful CategoryTheory.Limits.IsLimit.ofFaithful
 
+#print CategoryTheory.Limits.IsLimit.mapConeEquiv /-
 /-- If `F` and `G` are naturally isomorphic, then `F.map_cone c` being a limit implies
 `G.map_cone c` is also a limit.
 -/
@@ -452,7 +645,9 @@ def mapConeEquiv {D : Type u₄} [Category.{v₄} D] {K : J ⥤ C} {F G : C ⥤
   apply postcompose_inv_equiv (iso_whisker_left K h : _) (G.map_cone c) _
   apply t.of_iso_limit (postcompose_whisker_left_map_cone h.symm c).symm
 #align category_theory.limits.is_limit.map_cone_equiv CategoryTheory.Limits.IsLimit.mapConeEquiv
+-/
 
+#print CategoryTheory.Limits.IsLimit.isoUniqueConeMorphism /-
 /-- A cone is a limit cone exactly if
 there is a unique cone morphism from any other cone.
 -/
@@ -463,13 +658,20 @@ def isoUniqueConeMorphism {t : Cone F} : IsLimit t ≅ ∀ s, Unique (s ⟶ t)
       uniq := fun _ => h.uniq_cone_morphism }
   inv h :=
     { lift := fun s => (h s).default.Hom
-      uniq' := fun s f w => congr_arg ConeMorphism.hom ((h s).uniq ⟨f, w⟩) }
+      uniq := fun s f w => congr_arg ConeMorphism.hom ((h s).uniq ⟨f, w⟩) }
 #align category_theory.limits.is_limit.iso_unique_cone_morphism CategoryTheory.Limits.IsLimit.isoUniqueConeMorphism
+-/
 
 namespace OfNatIso
 
 variable {X : C} (h : yoneda.obj X ⋙ uliftFunctor.{u₁} ≅ F.cones)
 
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 /-- If `F.cones` is represented by `X`, each morphism `f : Y ⟶ X` gives a cone with cone point
 `Y`. -/
 def coneOfHom {Y : C} (f : Y ⟶ X) : Cone F where
@@ -477,30 +679,60 @@ def coneOfHom {Y : C} (f : Y ⟶ X) : Cone F where
   π := h.Hom.app (op Y) ⟨f⟩
 #align category_theory.limits.is_limit.of_nat_iso.cone_of_hom CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom
 
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 /-- If `F.cones` is represented by `X`, each cone `s` gives a morphism `s.X ⟶ X`. -/
 def homOfCone (s : Cone F) : s.x ⟶ X :=
   (h.inv.app (op s.x) s.π).down
 #align category_theory.limits.is_limit.of_nat_iso.hom_of_cone CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone
 
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 @[simp]
-theorem coneOfHom_of_cone (s : Cone F) : coneOfHom h (homOfCone h s) = s :=
+theorem coneOfHom_homOfCone (s : Cone F) : coneOfHom h (homOfCone h s) = s :=
   by
   dsimp [cone_of_hom, hom_of_cone]; cases s; congr ; dsimp
   convert congr_fun (congr_fun (congr_arg nat_trans.app h.inv_hom_id) (op s_X)) s_π
   exact ULift.up_down _
-#align category_theory.limits.is_limit.of_nat_iso.cone_of_hom_of_cone CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_of_cone
-
+#align category_theory.limits.is_limit.of_nat_iso.cone_of_hom_of_cone CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_homOfCone
+
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_nat_iso.hom_of_cone_of_hom CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone_coneOfHomₓ'. -/
 @[simp]
-theorem homOfCone_of_hom {Y : C} (f : Y ⟶ X) : homOfCone h (coneOfHom h f) = f :=
+theorem homOfCone_coneOfHom {Y : C} (f : Y ⟶ X) : homOfCone h (coneOfHom h f) = f :=
   congr_arg ULift.down (congr_fun (congr_fun (congr_arg NatTrans.app h.hom_inv_id) (op Y)) ⟨f⟩ : _)
-#align category_theory.limits.is_limit.of_nat_iso.hom_of_cone_of_hom CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone_of_hom
-
+#align category_theory.limits.is_limit.of_nat_iso.hom_of_cone_of_hom CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone_coneOfHom
+
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 /-- If `F.cones` is represented by `X`, the cone corresponding to the identity morphism on `X`
 will be a limit cone. -/
 def limitCone : Cone F :=
   coneOfHom h (𝟙 X)
 #align category_theory.limits.is_limit.of_nat_iso.limit_cone CategoryTheory.Limits.IsLimit.OfNatIso.limitCone
 
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 /-- If `F.cones` is represented by `X`, the cone corresponding to a morphism `f : Y ⟶ X` is
 the limit cone extended by `f`. -/
 theorem coneOfHom_fac {Y : C} (f : Y ⟶ X) : coneOfHom h f = (limitCone h).extend f :=
@@ -514,6 +746,12 @@ theorem coneOfHom_fac {Y : C} (f : Y ⟶ X) : coneOfHom h f = (limitCone h).exte
   rfl
 #align category_theory.limits.is_limit.of_nat_iso.cone_of_hom_fac CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_fac
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_nat_iso.cone_fac CategoryTheory.Limits.IsLimit.OfNatIso.cone_facₓ'. -/
 /-- If `F.cones` is represented by `X`, any cone is the extension of the limit cone by the
 corresponding morphism. -/
 theorem cone_fac (s : Cone F) : (limitCone h).extend (homOfCone h s) = s :=
@@ -529,19 +767,25 @@ section
 
 open OfNatIso
 
+/- warning: category_theory.limits.is_limit.of_nat_iso -> CategoryTheory.Limits.IsLimit.ofNatIso is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_limit.of_nat_iso CategoryTheory.Limits.IsLimit.ofNatIsoₓ'. -/
 /-- If `F.cones` is representable, then the cone corresponding to the identity morphism on
 the representing object is a limit cone.
 -/
 def ofNatIso {X : C} (h : yoneda.obj X ⋙ uliftFunctor.{u₁} ≅ F.cones) : IsLimit (limitCone h)
     where
   lift s := homOfCone h s
-  fac' s j := by
+  fac s j := by
     have h := cone_fac h s
     cases s
     injection h with h₁ h₂
     simp only [heq_iff_eq] at h₂
     conv_rhs => rw [← h₂]; rfl
-  uniq' s m w := by
+  uniq s m w := by
     rw [← hom_of_cone_of_hom h m]
     congr
     rw [cone_of_hom_fac]
@@ -552,6 +796,7 @@ end
 
 end IsLimit
 
+#print CategoryTheory.Limits.IsColimit /-
 /-- A cocone `t` on `F` is a colimit cocone if each cocone on `F` admits a unique
 cocone morphism from `t`.
 
@@ -560,11 +805,11 @@ See <https://stacks.math.columbia.edu/tag/002F>.
 @[nolint has_nonempty_instance]
 structure IsColimit (t : Cocone F) where
   desc : ∀ s : Cocone F, t.x ⟶ s.x
-  fac' : ∀ (s : Cocone F) (j : J), t.ι.app j ≫ desc s = s.ι.app j := by obviously
-  uniq' :
-    ∀ (s : Cocone F) (m : t.x ⟶ s.x) (w : ∀ j : J, t.ι.app j ≫ m = s.ι.app j), m = desc s := by
+  fac : ∀ (s : Cocone F) (j : J), t.ι.app j ≫ desc s = s.ι.app j := by obviously
+  uniq : ∀ (s : Cocone F) (m : t.x ⟶ s.x) (w : ∀ j : J, t.ι.app j ≫ m = s.ι.app j), m = desc s := by
     obviously
 #align category_theory.limits.is_colimit CategoryTheory.Limits.IsColimit
+-/
 
 restate_axiom is_colimit.fac'
 
@@ -574,44 +819,72 @@ restate_axiom is_colimit.uniq'
 
 namespace IsColimit
 
+#print CategoryTheory.Limits.IsColimit.subsingleton /-
 instance subsingleton {t : Cocone F} : Subsingleton (IsColimit t) :=
   ⟨by intro P Q <;> cases P <;> cases Q <;> congr <;> ext <;> solve_by_elim⟩
 #align category_theory.limits.is_colimit.subsingleton CategoryTheory.Limits.IsColimit.subsingleton
+-/
 
+#print CategoryTheory.Limits.IsColimit.map /-
 /-- Given a natural transformation `α : F ⟶ G`, we give a morphism from the cocone point
 of a colimit cocone over `F` to the cocone point of any cocone over `G`. -/
 def map {F G : J ⥤ C} {s : Cocone F} (P : IsColimit s) (t : Cocone G) (α : F ⟶ G) : s.x ⟶ t.x :=
   P.desc ((Cocones.precompose α).obj t)
 #align category_theory.limits.is_colimit.map CategoryTheory.Limits.IsColimit.map
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.ι_map CategoryTheory.Limits.IsColimit.ι_mapₓ'. -/
 @[simp, reassoc.1]
 theorem ι_map {F G : J ⥤ C} {c : Cocone F} (hc : IsColimit c) (d : Cocone G) (α : F ⟶ G) (j : J) :
     c.ι.app j ≫ IsColimit.map hc d α = α.app j ≫ d.ι.app j :=
   fac _ _ _
 #align category_theory.limits.is_colimit.ι_map CategoryTheory.Limits.IsColimit.ι_map
 
+#print CategoryTheory.Limits.IsColimit.desc_self /-
 @[simp]
 theorem desc_self {t : Cocone F} (h : IsColimit t) : h.desc t = 𝟙 t.x :=
   (h.uniq _ _ fun j => comp_id _).symm
 #align category_theory.limits.is_colimit.desc_self CategoryTheory.Limits.IsColimit.desc_self
+-/
 
+#print CategoryTheory.Limits.IsColimit.descCoconeMorphism /-
 -- Repackaging the definition in terms of cocone morphisms.
 /-- The universal morphism from a colimit cocone to any other cocone. -/
 @[simps]
 def descCoconeMorphism {t : Cocone F} (h : IsColimit t) (s : Cocone F) : t ⟶ s where Hom := h.desc s
 #align category_theory.limits.is_colimit.desc_cocone_morphism CategoryTheory.Limits.IsColimit.descCoconeMorphism
+-/
 
+#print CategoryTheory.Limits.IsColimit.uniq_cocone_morphism /-
 theorem uniq_cocone_morphism {s t : Cocone F} (h : IsColimit t) {f f' : t ⟶ s} : f = f' :=
   have : ∀ {g : t ⟶ s}, g = h.descCoconeMorphism s := by intro g <;> ext <;> exact h.uniq _ _ g.w
   this.trans this.symm
 #align category_theory.limits.is_colimit.uniq_cocone_morphism CategoryTheory.Limits.IsColimit.uniq_cocone_morphism
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.exists_unique CategoryTheory.Limits.IsColimit.existsUniqueₓ'. -/
 /-- Restating the definition of a colimit cocone in terms of the ∃! operator. -/
 theorem existsUnique {t : Cocone F} (h : IsColimit t) (s : Cocone F) :
     ∃! d : t.x ⟶ s.x, ∀ j, t.ι.app j ≫ d = s.ι.app j :=
   ⟨h.desc s, h.fac s, h.uniq s⟩
 #align category_theory.limits.is_colimit.exists_unique CategoryTheory.Limits.IsColimit.existsUnique
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_exists_unique CategoryTheory.Limits.IsColimit.ofExistsUniqueₓ'. -/
 /-- Noncomputably make a colimit cocone from the existence of unique factorizations. -/
 def ofExistsUnique {t : Cocone F}
     (ht : ∀ s : Cocone F, ∃! d : t.x ⟶ s.x, ∀ j, t.ι.app j ≫ d = s.ι.app j) : IsColimit t :=
@@ -620,6 +893,7 @@ def ofExistsUnique {t : Cocone F}
   exact ⟨s, hs, hs'⟩
 #align category_theory.limits.is_colimit.of_exists_unique CategoryTheory.Limits.IsColimit.ofExistsUnique
 
+#print CategoryTheory.Limits.IsColimit.mkCoconeMorphism /-
 /-- Alternative constructor for `is_colimit`,
 providing a morphism of cocones rather than a morphism between the cocone points
 and separately the factorisation condition.
@@ -629,11 +903,13 @@ def mkCoconeMorphism {t : Cocone F} (desc : ∀ s : Cocone F, t ⟶ s)
     (uniq' : ∀ (s : Cocone F) (m : t ⟶ s), m = desc s) : IsColimit t
     where
   desc s := (desc s).Hom
-  uniq' s m w :=
+  uniq s m w :=
     have : CoconeMorphism.mk m w = desc s := by apply uniq'
     congr_arg CoconeMorphism.hom this
 #align category_theory.limits.is_colimit.mk_cocone_morphism CategoryTheory.Limits.IsColimit.mkCoconeMorphism
+-/
 
+#print CategoryTheory.Limits.IsColimit.uniqueUpToIso /-
 /-- Colimit cocones on `F` are unique up to isomorphism. -/
 @[simps]
 def uniqueUpToIso {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t) : s ≅ t
@@ -643,53 +919,79 @@ def uniqueUpToIso {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t) : s ≅ t
   hom_inv_id' := P.uniq_cocone_morphism
   inv_hom_id' := Q.uniq_cocone_morphism
 #align category_theory.limits.is_colimit.unique_up_to_iso CategoryTheory.Limits.IsColimit.uniqueUpToIso
+-/
 
+#print CategoryTheory.Limits.IsColimit.hom_isIso /-
 /-- Any cocone morphism between colimit cocones is an isomorphism. -/
 theorem hom_isIso {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t) (f : s ⟶ t) : IsIso f :=
   ⟨⟨Q.descCoconeMorphism s, ⟨P.uniq_cocone_morphism, Q.uniq_cocone_morphism⟩⟩⟩
 #align category_theory.limits.is_colimit.hom_is_iso CategoryTheory.Limits.IsColimit.hom_isIso
+-/
 
+#print CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso /-
 /-- Colimits of `F` are unique up to isomorphism. -/
 def coconePointUniqueUpToIso {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t) : s.x ≅ t.x :=
   (Cocones.forget F).mapIso (uniqueUpToIso P Q)
 #align category_theory.limits.is_colimit.cocone_point_unique_up_to_iso CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_hom CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_homₓ'. -/
 @[simp, reassoc.1]
 theorem comp_coconePointUniqueUpToIso_hom {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t)
     (j : J) : s.ι.app j ≫ (coconePointUniqueUpToIso P Q).Hom = t.ι.app j :=
   (uniqueUpToIso P Q).Hom.w _
 #align category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_hom CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_inv CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_invₓ'. -/
 @[simp, reassoc.1]
 theorem comp_coconePointUniqueUpToIso_inv {s t : Cocone F} (P : IsColimit s) (Q : IsColimit t)
     (j : J) : t.ι.app j ≫ (coconePointUniqueUpToIso P Q).inv = s.ι.app j :=
   (uniqueUpToIso P Q).inv.w _
 #align category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_inv CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv
 
+#print CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc /-
 @[simp, reassoc.1]
 theorem coconePointUniqueUpToIso_hom_desc {r s t : Cocone F} (P : IsColimit s) (Q : IsColimit t) :
     (coconePointUniqueUpToIso P Q).Hom ≫ Q.desc r = P.desc r :=
   P.uniq _ _ (by simp)
 #align category_theory.limits.is_colimit.cocone_point_unique_up_to_iso_hom_desc CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc
+-/
 
+#print CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_inv_desc /-
 @[simp, reassoc.1]
 theorem coconePointUniqueUpToIso_inv_desc {r s t : Cocone F} (P : IsColimit s) (Q : IsColimit t) :
     (coconePointUniqueUpToIso P Q).inv ≫ P.desc r = Q.desc r :=
   Q.uniq _ _ (by simp)
 #align category_theory.limits.is_colimit.cocone_point_unique_up_to_iso_inv_desc CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_inv_desc
+-/
 
+#print CategoryTheory.Limits.IsColimit.ofIsoColimit /-
 /-- Transport evidence that a cocone is a colimit cocone across an isomorphism of cocones. -/
 def ofIsoColimit {r t : Cocone F} (P : IsColimit r) (i : r ≅ t) : IsColimit t :=
   IsColimit.mkCoconeMorphism (fun s => i.inv ≫ P.descCoconeMorphism s) fun s m => by
     rw [i.eq_inv_comp] <;> apply P.uniq_cocone_morphism
 #align category_theory.limits.is_colimit.of_iso_colimit CategoryTheory.Limits.IsColimit.ofIsoColimit
+-/
 
+#print CategoryTheory.Limits.IsColimit.ofIsoColimit_desc /-
 @[simp]
 theorem ofIsoColimit_desc {r t : Cocone F} (P : IsColimit r) (i : r ≅ t) (s) :
     (P.ofIsoColimit i).desc s = i.inv.Hom ≫ P.desc s :=
   rfl
 #align category_theory.limits.is_colimit.of_iso_colimit_desc CategoryTheory.Limits.IsColimit.ofIsoColimit_desc
+-/
 
+#print CategoryTheory.Limits.IsColimit.equivIsoColimit /-
 /-- Isomorphism of cocones preserves whether or not they are colimiting cocones. -/
 def equivIsoColimit {r t : Cocone F} (i : r ≅ t) : IsColimit r ≃ IsColimit t
     where
@@ -698,19 +1000,25 @@ def equivIsoColimit {r t : Cocone F} (i : r ≅ t) : IsColimit r ≃ IsColimit t
   left_inv := by tidy
   right_inv := by tidy
 #align category_theory.limits.is_colimit.equiv_iso_colimit CategoryTheory.Limits.IsColimit.equivIsoColimit
+-/
 
+#print CategoryTheory.Limits.IsColimit.equivIsoColimit_apply /-
 @[simp]
 theorem equivIsoColimit_apply {r t : Cocone F} (i : r ≅ t) (P : IsColimit r) :
     equivIsoColimit i P = P.ofIsoColimit i :=
   rfl
 #align category_theory.limits.is_colimit.equiv_iso_colimit_apply CategoryTheory.Limits.IsColimit.equivIsoColimit_apply
+-/
 
+#print CategoryTheory.Limits.IsColimit.equivIsoColimit_symm_apply /-
 @[simp]
 theorem equivIsoColimit_symm_apply {r t : Cocone F} (i : r ≅ t) (P : IsColimit t) :
     (equivIsoColimit i).symm P = P.ofIsoColimit i.symm :=
   rfl
 #align category_theory.limits.is_colimit.equiv_iso_colimit_symm_apply CategoryTheory.Limits.IsColimit.equivIsoColimit_symm_apply
+-/
 
+#print CategoryTheory.Limits.IsColimit.ofPointIso /-
 /-- If the canonical morphism to a cocone point from a colimiting cocone point is an iso, then the
 first cocone was colimiting also.
 -/
@@ -721,9 +1029,16 @@ def ofPointIso {r t : Cocone F} (P : IsColimit r) [i : IsIso (P.desc t)] : IsCol
       haveI : is_iso (P.desc_cocone_morphism t) := cocones.cocone_iso_of_hom_iso _
       apply as_iso (P.desc_cocone_morphism t))
 #align category_theory.limits.is_colimit.of_point_iso CategoryTheory.Limits.IsColimit.ofPointIso
+-/
 
 variable {t : Cocone F}
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.hom_desc CategoryTheory.Limits.IsColimit.hom_descₓ'. -/
 theorem hom_desc (h : IsColimit t) {W : C} (m : t.x ⟶ W) :
     m =
       h.desc
@@ -739,6 +1054,12 @@ theorem hom_desc (h : IsColimit t) {W : C} (m : t.x ⟶ W) :
     m fun b => rfl
 #align category_theory.limits.is_colimit.hom_desc CategoryTheory.Limits.IsColimit.hom_desc
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.hom_ext CategoryTheory.Limits.IsColimit.hom_extₓ'. -/
 /-- Two morphisms out of a colimit are equal if their compositions with
   each cocone morphism are equal. -/
 theorem hom_ext (h : IsColimit t) {W : C} {f f' : t.x ⟶ W}
@@ -746,6 +1067,12 @@ theorem hom_ext (h : IsColimit t) {W : C} {f f' : t.x ⟶ W}
   rw [h.hom_desc f, h.hom_desc f'] <;> congr <;> exact funext w
 #align category_theory.limits.is_colimit.hom_ext CategoryTheory.Limits.IsColimit.hom_ext
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_left_adjoint CategoryTheory.Limits.IsColimit.ofLeftAdjointₓ'. -/
 /-- Given a left adjoint functor between categories of cocones,
 the image of a colimit cocone is a colimit cocone.
 -/
@@ -756,6 +1083,12 @@ def ofLeftAdjoint {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cocone
     (Adjunction.homEquiv_apply_eq _ _ _).1 t.uniq_cocone_morphism
 #align category_theory.limits.is_colimit.of_left_adjoint CategoryTheory.Limits.IsColimit.ofLeftAdjoint
 
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 /-- Given two functors which have equivalent categories of cocones,
 we can transport a colimiting cocone across the equivalence.
 -/
@@ -768,6 +1101,12 @@ def ofCoconeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cocone
   right_inv := by tidy
 #align category_theory.limits.is_colimit.of_cocone_equiv CategoryTheory.Limits.IsColimit.ofCoconeEquiv
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_cocone_equiv_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_descₓ'. -/
 @[simp]
 theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
     (h : Cocone G ≌ Cocone F) {c : Cocone G} (P : IsColimit (h.Functor.obj c)) (s) :
@@ -777,6 +1116,12 @@ theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤
   rfl
 #align category_theory.limits.is_colimit.of_cocone_equiv_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc
 
+/- warning: category_theory.limits.is_colimit.of_cocone_equiv_symm_apply_desc -> CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_cocone_equiv_symm_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_descₓ'. -/
 @[simp]
 theorem ofCoconeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
     (h : Cocone G ≌ Cocone F) {c : Cocone G} (P : IsColimit c) (s) :
@@ -785,6 +1130,12 @@ theorem ofCoconeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K
   rfl
 #align category_theory.limits.is_colimit.of_cocone_equiv_symm_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc
 
+/- warning: category_theory.limits.is_colimit.precompose_hom_equiv -> CategoryTheory.Limits.IsColimit.precomposeHomEquiv is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.precompose_hom_equiv CategoryTheory.Limits.IsColimit.precomposeHomEquivₓ'. -/
 /-- A cocone precomposed with a natural isomorphism is a colimit cocone
 if and only if the original cocone is.
 -/
@@ -793,6 +1144,12 @@ def precomposeHomEquiv {F G : J ⥤ C} (α : F ≅ G) (c : Cocone G) :
   ofCoconeEquiv (Cocones.precomposeEquivalence α)
 #align category_theory.limits.is_colimit.precompose_hom_equiv CategoryTheory.Limits.IsColimit.precomposeHomEquiv
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.precompose_inv_equiv CategoryTheory.Limits.IsColimit.precomposeInvEquivₓ'. -/
 /-- A cocone precomposed with the inverse of a natural isomorphism is a colimit cocone
 if and only if the original cocone is.
 -/
@@ -801,6 +1158,12 @@ def precomposeInvEquiv {F G : J ⥤ C} (α : F ≅ G) (c : Cocone F) :
   precomposeHomEquiv α.symm c
 #align category_theory.limits.is_colimit.precompose_inv_equiv CategoryTheory.Limits.IsColimit.precomposeInvEquiv
 
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 /-- Constructing an equivalence `is_colimit c ≃ is_colimit d` from a natural isomorphism
 between the underlying functors, and then an isomorphism between `c` transported along this and `d`.
 -/
@@ -809,6 +1172,7 @@ def equivOfNatIsoOfIso {F G : J ⥤ C} (α : F ≅ G) (c : Cocone F) (d : Cocone
   (precomposeInvEquiv α _).symm.trans (equivIsoColimit w)
 #align category_theory.limits.is_colimit.equiv_of_nat_iso_of_iso CategoryTheory.Limits.IsColimit.equivOfNatIsoOfIso
 
+#print CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso /-
 /-- The cocone points of two colimit cocones for naturally isomorphic functors
 are themselves isomorphic.
 -/
@@ -821,37 +1185,60 @@ def coconePointsIsoOfNatIso {F G : J ⥤ C} {s : Cocone F} {t : Cocone G} (P : I
   hom_inv_id' := P.hom_ext (by tidy)
   inv_hom_id' := Q.hom_ext (by tidy)
 #align category_theory.limits.is_colimit.cocone_points_iso_of_nat_iso CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_hom CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_homₓ'. -/
 @[reassoc.1]
 theorem comp_coconePointsIsoOfNatIso_hom {F G : J ⥤ C} {s : Cocone F} {t : Cocone G}
     (P : IsColimit s) (Q : IsColimit t) (w : F ≅ G) (j : J) :
     s.ι.app j ≫ (coconePointsIsoOfNatIso P Q w).Hom = w.Hom.app j ≫ t.ι.app j := by simp
 #align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_hom CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_inv CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_invₓ'. -/
 @[reassoc.1]
 theorem comp_coconePointsIsoOfNatIso_inv {F G : J ⥤ C} {s : Cocone F} {t : Cocone G}
     (P : IsColimit s) (Q : IsColimit t) (w : F ≅ G) (j : J) :
     t.ι.app j ≫ (coconePointsIsoOfNatIso P Q w).inv = w.inv.app j ≫ s.ι.app j := by simp
 #align category_theory.limits.is_colimit.comp_cocone_points_iso_of_nat_iso_inv CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv
 
+#print CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc /-
 @[reassoc.1]
 theorem coconePointsIsoOfNatIso_hom_desc {F G : J ⥤ C} {s : Cocone F} {r t : Cocone G}
     (P : IsColimit s) (Q : IsColimit t) (w : F ≅ G) :
     (coconePointsIsoOfNatIso P Q w).Hom ≫ Q.desc r = P.map _ w.Hom :=
   P.hom_ext (by simp)
 #align category_theory.limits.is_colimit.cocone_points_iso_of_nat_iso_hom_desc CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc
+-/
 
+#print CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc /-
 @[reassoc.1]
 theorem coconePointsIsoOfNatIso_inv_desc {F G : J ⥤ C} {s : Cocone G} {r t : Cocone F}
     (P : IsColimit t) (Q : IsColimit s) (w : F ≅ G) :
     (coconePointsIsoOfNatIso P Q w).inv ≫ P.desc r = Q.map _ w.inv :=
   Q.hom_ext (by simp)
 #align category_theory.limits.is_colimit.cocone_points_iso_of_nat_iso_inv_desc CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc
+-/
 
 section Equivalence
 
 open CategoryTheory.Equivalence
 
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 /-- If `s : cocone F` is a colimit cocone, so is `s` whiskered by an equivalence `e`.
 -/
 def whiskerEquivalence {s : Cocone F} (P : IsColimit s) (e : K ≌ J) :
@@ -859,6 +1246,12 @@ def whiskerEquivalence {s : Cocone F} (P : IsColimit s) (e : K ≌ J) :
   ofLeftAdjoint (Cocones.whiskeringEquivalence e).Functor P
 #align category_theory.limits.is_colimit.whisker_equivalence CategoryTheory.Limits.IsColimit.whiskerEquivalence
 
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 /-- If `s : cocone F` whiskered by an equivalence `e` is a colimit cocone, so is `s`.
 -/
 def ofWhiskerEquivalence {s : Cocone F} (e : K ≌ J) (P : IsColimit (s.whisker e.Functor)) :
@@ -867,6 +1260,12 @@ def ofWhiskerEquivalence {s : Cocone F} (e : K ≌ J) (P : IsColimit (s.whisker
     (ofLeftAdjoint (Cocones.whiskeringEquivalence e).inverse P : _)
 #align category_theory.limits.is_colimit.of_whisker_equivalence CategoryTheory.Limits.IsColimit.ofWhiskerEquivalence
 
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 /-- Given an equivalence of diagrams `e`, `s` is a colimit cocone iff `s.whisker e.functor` is.
 -/
 def whiskerEquivalenceEquiv {s : Cocone F} (e : K ≌ J) :
@@ -874,6 +1273,12 @@ def whiskerEquivalenceEquiv {s : Cocone F} (e : K ≌ J) :
   ⟨fun h => h.whiskerEquivalence e, ofWhiskerEquivalence e, by tidy, by tidy⟩
 #align category_theory.limits.is_colimit.whisker_equivalence_equiv CategoryTheory.Limits.IsColimit.whiskerEquivalenceEquiv
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.cocone_points_iso_of_equivalence CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalenceₓ'. -/
 /-- We can prove two cocone points `(s : cocone F).X` and `(t.cocone G).X` are isomorphic if
 * both cocones are colimit cocones
 * their indexing categories are equivalent via some `e : J ≌ K`,
@@ -904,6 +1309,12 @@ def coconePointsIsoOfEquivalence {F : J ⥤ C} {s : Cocone F} {G : K ⥤ C} {t :
 
 end Equivalence
 
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 /-- The universal property of a colimit cocone: a map `X ⟶ W` is the same as
   a cocone on `F` with vertex `W`. -/
 def homIso (h : IsColimit t) (W : C) : ULift.{u₁} (t.x ⟶ W : Type v₃) ≅ F ⟶ (const J).obj W
@@ -916,18 +1327,36 @@ def homIso (h : IsColimit t) (W : C) : ULift.{u₁} (t.x ⟶ W : Type v₃) ≅
   hom_inv_id' := by ext f <;> apply h.hom_ext <;> intro j <;> simp <;> dsimp <;> rfl
 #align category_theory.limits.is_colimit.hom_iso CategoryTheory.Limits.IsColimit.homIso
 
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 @[simp]
 theorem homIso_hom (h : IsColimit t) {W : C} (f : ULift (t.x ⟶ W)) :
     (IsColimit.homIso h W).Hom f = (t.extend f.down).ι :=
   rfl
 #align category_theory.limits.is_colimit.hom_iso_hom CategoryTheory.Limits.IsColimit.homIso_hom
 
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 /-- The colimit of `F` represents the functor taking `W` to
   the set of cocones on `F` with vertex `W`. -/
 def natIso (h : IsColimit t) : coyoneda.obj (op t.x) ⋙ uliftFunctor.{u₁} ≅ F.cocones :=
   NatIso.ofComponents (IsColimit.homIso h) (by intros <;> ext <;> dsimp <;> rw [← assoc] <;> rfl)
 #align category_theory.limits.is_colimit.nat_iso CategoryTheory.Limits.IsColimit.natIso
 
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 /-- Another, more explicit, formulation of the universal property of a colimit cocone.
 See also `hom_iso`.
 -/
@@ -942,6 +1371,12 @@ def homIso' (h : IsColimit t) (W : C) :
           naturality' := fun j j' f => by dsimp; rw [comp_id]; exact p.2 f } }
 #align category_theory.limits.is_colimit.hom_iso' CategoryTheory.Limits.IsColimit.homIso'
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_faithful CategoryTheory.Limits.IsColimit.ofFaithfulₓ'. -/
 /-- If G : C → D is a faithful functor which sends t to a colimit cocone,
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/
@@ -949,14 +1384,15 @@ def ofFaithful {t : Cocone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D)
     (ht : IsColimit (G.mapCocone t)) (desc : ∀ s : Cocone F, t.x ⟶ s.x)
     (h : ∀ s, G.map (desc s) = ht.desc (G.mapCocone s)) : IsColimit t :=
   { desc
-    fac' := fun s j => by apply G.map_injective <;> rw [G.map_comp, h] <;> apply ht.fac
-    uniq' := fun s m w => by
+    fac := fun s j => by apply G.map_injective <;> rw [G.map_comp, h] <;> apply ht.fac
+    uniq := fun s m w => by
       apply G.map_injective; rw [h]
       refine' ht.uniq (G.map_cocone s) _ fun j => _
       convert ← congr_arg (fun f => G.map f) (w j)
       apply G.map_comp }
 #align category_theory.limits.is_colimit.of_faithful CategoryTheory.Limits.IsColimit.ofFaithful
 
+#print CategoryTheory.Limits.IsColimit.mapCoconeEquiv /-
 /-- If `F` and `G` are naturally isomorphic, then `F.map_cone c` being a colimit implies
 `G.map_cone c` is also a colimit.
 -/
@@ -966,7 +1402,9 @@ def mapCoconeEquiv {D : Type u₄} [Category.{v₄} D] {K : J ⥤ C} {F G : C 
   apply is_colimit.of_iso_colimit _ (precompose_whisker_left_map_cocone h c)
   apply (precompose_inv_equiv (iso_whisker_left K h : _) _).symm t
 #align category_theory.limits.is_colimit.map_cocone_equiv CategoryTheory.Limits.IsColimit.mapCoconeEquiv
+-/
 
+#print CategoryTheory.Limits.IsColimit.isoUniqueCoconeMorphism /-
 /-- A cocone is a colimit cocone exactly if
 there is a unique cocone morphism from any other cocone.
 -/
@@ -977,13 +1415,20 @@ def isoUniqueCoconeMorphism {t : Cocone F} : IsColimit t ≅ ∀ s, Unique (t 
       uniq := fun _ => h.uniq_cocone_morphism }
   inv h :=
     { desc := fun s => (h s).default.Hom
-      uniq' := fun s f w => congr_arg CoconeMorphism.hom ((h s).uniq ⟨f, w⟩) }
+      uniq := fun s f w => congr_arg CoconeMorphism.hom ((h s).uniq ⟨f, w⟩) }
 #align category_theory.limits.is_colimit.iso_unique_cocone_morphism CategoryTheory.Limits.IsColimit.isoUniqueCoconeMorphism
+-/
 
 namespace OfNatIso
 
 variable {X : C} (h : coyoneda.obj (op X) ⋙ uliftFunctor.{u₁} ≅ F.cocones)
 
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 /-- If `F.cocones` is corepresented by `X`, each morphism `f : X ⟶ Y` gives a cocone with cone
 point `Y`. -/
 def coconeOfHom {Y : C} (f : X ⟶ Y) : Cocone F
@@ -992,30 +1437,60 @@ def coconeOfHom {Y : C} (f : X ⟶ Y) : Cocone F
   ι := h.Hom.app Y ⟨f⟩
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom
 
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 /-- If `F.cocones` is corepresented by `X`, each cocone `s` gives a morphism `X ⟶ s.X`. -/
 def homOfCocone (s : Cocone F) : X ⟶ s.x :=
   (h.inv.app s.x s.ι).down
 #align category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone
 
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 @[simp]
-theorem coconeOfHom_of_cocone (s : Cocone F) : coconeOfHom h (homOfCocone h s) = s :=
+theorem coconeOfHom_homOfCocone (s : Cocone F) : coconeOfHom h (homOfCocone h s) = s :=
   by
   dsimp [cocone_of_hom, hom_of_cocone]; cases s; congr ; dsimp
   convert congr_fun (congr_fun (congr_arg nat_trans.app h.inv_hom_id) s_X) s_ι
   exact ULift.up_down _
-#align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_of_cocone CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_of_cocone
-
+#align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_of_cocone CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_homOfCocone
+
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 @[simp]
-theorem homOfCocone_of_hom {Y : C} (f : X ⟶ Y) : homOfCocone h (coconeOfHom h f) = f :=
+theorem homOfCocone_cooneOfHom {Y : C} (f : X ⟶ Y) : homOfCocone h (coconeOfHom h f) = f :=
   congr_arg ULift.down (congr_fun (congr_fun (congr_arg NatTrans.app h.hom_inv_id) Y) ⟨f⟩ : _)
-#align category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone_of_hom CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone_of_hom
-
+#align category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone_of_hom CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone_cooneOfHom
+
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 /-- If `F.cocones` is corepresented by `X`, the cocone corresponding to the identity morphism on `X`
 will be a colimit cocone. -/
 def colimitCocone : Cocone F :=
   coconeOfHom h (𝟙 X)
 #align category_theory.limits.is_colimit.of_nat_iso.colimit_cocone CategoryTheory.Limits.IsColimit.OfNatIso.colimitCocone
 
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 /-- If `F.cocones` is corepresented by `X`, the cocone corresponding to a morphism `f : Y ⟶ X` is
 the colimit cocone extended by `f`. -/
 theorem coconeOfHom_fac {Y : C} (f : X ⟶ Y) : coconeOfHom h f = (colimitCocone h).extend f :=
@@ -1029,6 +1504,12 @@ theorem coconeOfHom_fac {Y : C} (f : X ⟶ Y) : coconeOfHom h f = (colimitCocone
   rfl
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_fac CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_fac
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_nat_iso.cocone_fac CategoryTheory.Limits.IsColimit.OfNatIso.cocone_facₓ'. -/
 /-- If `F.cocones` is corepresented by `X`, any cocone is the extension of the colimit cocone by the
 corresponding morphism. -/
 theorem cocone_fac (s : Cocone F) : (colimitCocone h).extend (homOfCocone h s) = s :=
@@ -1044,19 +1525,25 @@ section
 
 open OfNatIso
 
+/- warning: category_theory.limits.is_colimit.of_nat_iso -> CategoryTheory.Limits.IsColimit.ofNatIso is a dubious translation:
+lean 3 declaration is
+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max u4 u2 u3, max u2 (max u2 u3) u4 (succ (max u2 u3))} (CategoryTheory.Functor.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u2 u3, u4, succ (max u2 u3)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u2 u3, u4, succ u2, succ (max u2 u3)} C _inst_3 Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.Functor.obj.{u2, max u4 u2, u4, max u2 u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.coyoneda.{u2, u4} C _inst_3) (Opposite.op.{succ u4} C X)) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cocones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)), CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.IsColimit.OfNatIso.colimitCocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h)
+but is expected to have type
+  forall {J : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} J] {C : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} C] {F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_1 C _inst_3} {X : C} (h : CategoryTheory.Iso.{max (max u3 u4) u2, max (max (max (max (succ u3) (succ u2)) u4) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u4, max (succ u3) (succ u2)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.category.{u2, max u3 u2, u4, max (succ u3) (succ u2)} C _inst_3 Type.{max u2 u3} CategoryTheory.types.{max u2 u3}) (CategoryTheory.Functor.comp.{u2, u2, max u3 u2, u4, succ u2, max (succ u3) (succ u2)} C _inst_3 Type.{u2} CategoryTheory.types.{u2} Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Prefunctor.obj.{succ u2, max (succ u4) (succ u2), u4, max u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Opposite.{succ u4} C) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3))) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max u4 (succ u2)} (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}))) (CategoryTheory.Functor.toPrefunctor.{u2, max u4 u2, u4, max u4 (succ u2)} (Opposite.{succ u4} C) (CategoryTheory.Category.opposite.{u2, u4} C _inst_3) (CategoryTheory.Functor.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.Functor.category.{u2, u2, u4, succ u2} C _inst_3 Type.{u2} CategoryTheory.types.{u2}) (CategoryTheory.coyoneda.{u2, u4} C _inst_3)) (Opposite.op.{succ u4} C X)) CategoryTheory.uliftFunctor.{u3, u2}) (CategoryTheory.Functor.cocones.{u1, u2, u3, u4} J _inst_1 C _inst_3 F)), CategoryTheory.Limits.IsColimit.{u1, u2, u3, u4} J _inst_1 C _inst_3 F (CategoryTheory.Limits.IsColimit.OfNatIso.colimitCocone.{u1, u2, u3, u4} J _inst_1 C _inst_3 F X h)
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_colimit.of_nat_iso CategoryTheory.Limits.IsColimit.ofNatIsoₓ'. -/
 /-- If `F.cocones` is corepresentable, then the cocone corresponding to the identity morphism on
 the representing object is a colimit cocone.
 -/
 def ofNatIso {X : C} (h : coyoneda.obj (op X) ⋙ uliftFunctor.{u₁} ≅ F.cocones) :
     IsColimit (colimitCocone h) where
   desc s := homOfCocone h s
-  fac' s j := by
+  fac s j := by
     have h := cocone_fac h s
     cases s
     injection h with h₁ h₂
     simp only [heq_iff_eq] at h₂
     conv_rhs => rw [← h₂]; rfl
-  uniq' s m w := by
+  uniq s m w := by
     rw [← hom_of_cocone_of_hom h m]
     congr
     rw [cocone_of_hom_fac]

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

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

@@ -51,7 +51,7 @@ cone morphism to `t`.
 
 See <https://stacks.math.columbia.edu/tag/002E>.
   -/
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 structure IsLimit (t : Cone F) where
   /-- There is a morphism from any cone point to `t.pt` -/
   lift : ∀ s : Cone F, s.pt ⟶ t.pt
@@ -566,7 +566,7 @@ cocone morphism from `t`.
 
 See <https://stacks.math.columbia.edu/tag/002F>.
 -/
--- Porting note: remove @[nolint has_nonempty_instance]
+-- Porting note(#5171): removed @[nolint has_nonempty_instance]
 structure IsColimit (t : Cocone F) where
   /-- `t.pt` maps to all other cocone covertices -/
   desc : ∀ s : Cocone F, t.pt ⟶ s.pt

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

@@ -443,7 +443,7 @@ def homIso' (h : IsLimit t) (W : C) :
 /-- If G : C → D is a faithful functor which sends t to a limit cone,
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/
-def ofFaithful {t : Cone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [Faithful G]
+def ofFaithful {t : Cone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [G.Faithful]
     (ht : IsLimit (mapCone G t)) (lift : ∀ s : Cone F, s.pt ⟶ t.pt)
     (h : ∀ s, G.map (lift s) = ht.lift (mapCone G s)) : IsLimit t :=
   { lift
@@ -972,7 +972,7 @@ def homIso' (h : IsColimit t) (W : C) :
 /-- If G : C → D is a faithful functor which sends t to a colimit cocone,
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/
-def ofFaithful {t : Cocone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [Faithful G]
+def ofFaithful {t : Cocone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D) [G.Faithful]
     (ht : IsColimit (mapCocone G t)) (desc : ∀ s : Cocone F, t.pt ⟶ s.pt)
     (h : ∀ s, G.map (desc s) = ht.desc (mapCocone G s)) : IsColimit t :=
   { desc

@@ -87,6 +87,7 @@ theorem map_π {F G : J ⥤ C} (c : Cone F) {d : Cone G} (hd : IsLimit d) (α :
   fac _ _ _
 #align category_theory.limits.is_limit.map_π CategoryTheory.Limits.IsLimit.map_π
 
+@[simp]
 theorem lift_self {c : Cone F} (t : IsLimit c) : t.lift c = 𝟙 c.pt :=
   (t.uniq _ _ fun _ => id_comp _).symm
 #align category_theory.limits.is_limit.lift_self CategoryTheory.Limits.IsLimit.lift_self

@@ -355,6 +355,21 @@ def whiskerEquivalenceEquiv {s : Cone F} (e : K ≌ J) : IsLimit s ≃ IsLimit (
   ⟨fun h => h.whiskerEquivalence e, ofWhiskerEquivalence e, by aesop_cat, by aesop_cat⟩
 #align category_theory.limits.is_limit.whisker_equivalence_equiv CategoryTheory.Limits.IsLimit.whiskerEquivalenceEquiv
 
+/-- A limit cone extended by an isomorphism is a limit cone. -/
+def extendIso {s : Cone F} {X : C} (i : X ⟶ s.pt) [IsIso i] (hs : IsLimit s) :
+    IsLimit (s.extend i) :=
+  IsLimit.ofIsoLimit hs (Cones.extendIso s (asIso i)).symm
+
+/-- A cone is a limit cone if its extension by an isomorphism is. -/
+def ofExtendIso {s : Cone F} {X : C} (i : X ⟶ s.pt) [IsIso i] (hs : IsLimit (s.extend i)) :
+    IsLimit s :=
+  IsLimit.ofIsoLimit hs (Cones.extendIso s (asIso i))
+
+/-- A cone is a limit cone iff its extension by an isomorphism is. -/
+def extendIsoEquiv {s : Cone F} {X : C} (i : X ⟶ s.pt) [IsIso i] :
+    IsLimit s ≃ IsLimit (s.extend i) :=
+  equivOfSubsingletonOfSubsingleton (extendIso i) (ofExtendIso i)
+
 /-- We can prove two cone points `(s : Cone F).pt` and `(t : Cone G).pt` are isomorphic if
 * both cones are limit cones
 * their indexing categories are equivalent via some `e : J ≌ K`,
@@ -869,6 +884,21 @@ def whiskerEquivalenceEquiv {s : Cocone F} (e : K ≌ J) :
   ⟨fun h => h.whiskerEquivalence e, ofWhiskerEquivalence e, by aesop_cat, by aesop_cat⟩
 #align category_theory.limits.is_colimit.whisker_equivalence_equiv CategoryTheory.Limits.IsColimit.whiskerEquivalenceEquiv
 
+/-- A colimit cocone extended by an isomorphism is a colimit cocone. -/
+def extendIso {s : Cocone F} {X : C} (i : s.pt ⟶ X) [IsIso i] (hs : IsColimit s) :
+    IsColimit (s.extend i) :=
+  IsColimit.ofIsoColimit hs (Cocones.extendIso s (asIso i))
+
+/-- A cocone is a colimit cocone if its extension by an isomorphism is. -/
+def ofExtendIso {s : Cocone F} {X : C} (i : s.pt ⟶ X) [IsIso i] (hs : IsColimit (s.extend i)) :
+    IsColimit s :=
+  IsColimit.ofIsoColimit hs (Cocones.extendIso s (asIso i)).symm
+
+/-- A cocone is a colimit cocone iff its extension by an isomorphism is. -/
+def extendIsoEquiv {s : Cocone F} {X : C} (i : s.pt ⟶ X) [IsIso i] :
+    IsColimit s ≃ IsColimit (s.extend i) :=
+  equivOfSubsingletonOfSubsingleton (extendIso i) (ofExtendIso i)
+
 /-- We can prove two cocone points `(s : Cocone F).pt` and `(t : Cocone G).pt` are isomorphic if
 * both cocones are colimit cocones
 * their indexing categories are equivalent via some `e : J ≌ K`,

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)

@@ -43,9 +43,7 @@ namespace CategoryTheory.Limits
 universe v₁ v₂ v₃ v₄ u₁ u₂ u₃ u₄
 
 variable {J : Type u₁} [Category.{v₁} J] {K : Type u₂} [Category.{v₂} K]
-
 variable {C : Type u₃} [Category.{v₃} C]
-
 variable {F : J ⥤ C}
 
 /-- A cone `t` on `F` is a limit cone if each cone on `F` admits a unique

@@ -111,7 +111,7 @@ theorem existsUnique {t : Cone F} (h : IsLimit t) (s : Cone F) :
   ⟨h.lift s, h.fac s, h.uniq s⟩
 #align category_theory.limits.is_limit.exists_unique CategoryTheory.Limits.IsLimit.existsUnique
 
-/-- Noncomputably make a colimit cocone from the existence of unique factorizations. -/
+/-- Noncomputably make a limit cone from the existence of unique factorizations. -/
 def ofExistsUnique {t : Cone F}
     (ht : ∀ s : Cone F, ∃! l : s.pt ⟶ t.pt, ∀ j, l ≫ t.π.app j = s.π.app j) : IsLimit t := by
   choose s hs hs' using ht

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -374,7 +374,7 @@ def conePointsIsoOfEquivalence {F : J ⥤ C} {s : Cone F} {G : K ⥤ C} {t : Con
     inv := P.lift ((Cones.equivalenceOfReindexing e w).functor.obj t)
     hom_inv_id := by
       apply hom_ext P; intro j
-      dsimp
+      dsimp [w']
       simp only [Limits.Cone.whisker_π, Limits.Cones.postcompose_obj_π, fac, whiskerLeft_app,
         assoc, id_comp, invFunIdAssoc_hom_app, fac_assoc, NatTrans.comp_app]
       rw [counit_app_functor, ← Functor.comp_map]
@@ -888,7 +888,7 @@ def coconePointsIsoOfEquivalence {F : J ⥤ C} {s : Cocone F} {G : K ⥤ C} {t :
     inv := Q.desc ((Cocones.equivalenceOfReindexing e.symm w').functor.obj s)
     hom_inv_id := by
       apply hom_ext P; intro j
-      dsimp
+      dsimp [w']
       simp only [Limits.Cocone.whisker_ι, fac, invFunIdAssoc_inv_app, whiskerLeft_app, assoc,
         comp_id, Limits.Cocones.precompose_obj_ι, fac_assoc, NatTrans.comp_app]
       rw [counitInv_app_functor, ← Functor.comp_map, ← w.inv.naturality_assoc]

Classifies by adding issue number (#10927) to porting notes claiming removed @[nolint has_nonempty_instance].

@@ -53,7 +53,7 @@ cone morphism to `t`.
 
 See <https://stacks.math.columbia.edu/tag/002E>.
   -/
--- Porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 structure IsLimit (t : Cone F) where
   /-- There is a morphism from any cone point to `t.pt` -/
   lift : ∀ s : Cone F, s.pt ⟶ t.pt

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

@@ -66,7 +66,7 @@ structure IsLimit (t : Cone F) where
 #align category_theory.limits.is_limit.fac' CategoryTheory.Limits.IsLimit.fac
 #align category_theory.limits.is_limit.uniq' CategoryTheory.Limits.IsLimit.uniq
 
--- Porting note:  simp can prove this. Linter complains it still exists
+-- Porting note (#10618):  simp can prove this. Linter complains it still exists
 attribute [-simp, nolint simpNF] IsLimit.mk.injEq
 
 attribute [reassoc (attr := simp)] IsLimit.fac
@@ -568,7 +568,7 @@ structure IsColimit (t : Cocone F) where
 
 attribute [reassoc (attr := simp)] IsColimit.fac
 
--- Porting note: simp can prove this. Linter claims it still is tagged with simp
+-- Porting note (#10618): simp can prove this. Linter claims it still is tagged with simp
 attribute [-simp, nolint simpNF] IsColimit.mk.injEq
 
 namespace IsColimit

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

@@ -377,7 +377,7 @@ def conePointsIsoOfEquivalence {F : J ⥤ C} {s : Cone F} {G : K ⥤ C} {t : Con
       dsimp
       simp only [Limits.Cone.whisker_π, Limits.Cones.postcompose_obj_π, fac, whiskerLeft_app,
         assoc, id_comp, invFunIdAssoc_hom_app, fac_assoc, NatTrans.comp_app]
-      rw [counit_app_functor, ←Functor.comp_map]
+      rw [counit_app_functor, ← Functor.comp_map]
       have l :
         NatTrans.app w.hom j = NatTrans.app w.hom (Prefunctor.obj (𝟭 J).toPrefunctor j) := by dsimp
       rw [l,w.hom.naturality]

aesop_cat_nonterminal is a non-terminal variant of aesop. It's not supposed to be used in production code since it's even worse than non-terminal simp. However, there were a few occurrences left (presumably from the port), which this PR removes.

The only nontrivial change is that I add mathlib's rfl tactic to the CategoryTheory Aesop rule set.

@@ -602,7 +602,7 @@ def descCoconeMorphism {t : Cocone F} (h : IsColimit t) (s : Cocone F) : t ⟶ s
 
 theorem uniq_cocone_morphism {s t : Cocone F} (h : IsColimit t) {f f' : t ⟶ s} : f = f' :=
   have : ∀ {g : t ⟶ s}, g = h.descCoconeMorphism s := by
-    intro g; aesop_cat_nonterminal; exact h.uniq _ _ g.w
+    intro g; ext; exact h.uniq _ _ g.w
   this.trans this.symm
 #align category_theory.limits.is_colimit.uniq_cocone_morphism CategoryTheory.Limits.IsColimit.uniq_cocone_morphism
 

@@ -96,7 +96,7 @@ theorem lift_self {c : Cone F} (t : IsLimit c) : t.lift c = 𝟙 c.pt :=
 -- Repackaging the definition in terms of cone morphisms.
 /-- The universal morphism from any other cone to a limit cone. -/
 @[simps]
-def liftConeMorphism {t : Cone F} (h : IsLimit t) (s : Cone F) : s ⟶ t where Hom := h.lift s
+def liftConeMorphism {t : Cone F} (h : IsLimit t) (s : Cone F) : s ⟶ t where hom := h.lift s
 #align category_theory.limits.is_limit.lift_cone_morphism CategoryTheory.Limits.IsLimit.liftConeMorphism
 
 theorem uniq_cone_morphism {s t : Cone F} (h : IsLimit t) {f f' : s ⟶ t} : f = f' :=
@@ -126,10 +126,10 @@ and separately the factorisation condition.
 def mkConeMorphism {t : Cone F} (lift : ∀ s : Cone F, s ⟶ t)
     (uniq : ∀ (s : Cone F) (m : s ⟶ t), m = lift s) : IsLimit t
     where
-  lift s := (lift s).Hom
+  lift s := (lift s).hom
   uniq s m w :=
     have : ConeMorphism.mk m w = lift s := by apply uniq
-    congrArg ConeMorphism.Hom this
+    congrArg ConeMorphism.hom this
 #align category_theory.limits.is_limit.mk_cone_morphism CategoryTheory.Limits.IsLimit.mkConeMorphism
 
 /-- Limit cones on `F` are unique up to isomorphism. -/
@@ -184,7 +184,7 @@ def ofIsoLimit {r t : Cone F} (P : IsLimit r) (i : r ≅ t) : IsLimit t :=
 
 @[simp]
 theorem ofIsoLimit_lift {r t : Cone F} (P : IsLimit r) (i : r ≅ t) (s) :
-    (P.ofIsoLimit i).lift s = P.lift s ≫ i.hom.Hom :=
+    (P.ofIsoLimit i).lift s = P.lift s ≫ i.hom.hom :=
   rfl
 #align category_theory.limits.is_limit.of_iso_limit_lift CategoryTheory.Limits.IsLimit.ofIsoLimit_lift
 
@@ -213,7 +213,7 @@ first cone was limiting also.
 -/
 def ofPointIso {r t : Cone F} (P : IsLimit r) [i : IsIso (P.lift t)] : IsLimit t :=
   ofIsoLimit P (by
-    haveI : IsIso (P.liftConeMorphism t).Hom := i
+    haveI : IsIso (P.liftConeMorphism t).hom := i
     haveI : IsIso (P.liftConeMorphism t) := Cones.cone_iso_of_hom_iso _
     symm
     apply asIso (P.liftConeMorphism t))
@@ -259,8 +259,8 @@ def ofConeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G 
 theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cone G ≌ Cone F)
     {c : Cone G} (P : IsLimit (h.functor.obj c)) (s) :
     (ofConeEquiv h P).lift s =
-      ((h.unitIso.hom.app s).Hom ≫ (h.functor.inv.map (P.liftConeMorphism (h.functor.obj s))).Hom) ≫
-        (h.unitIso.inv.app c).Hom :=
+      ((h.unitIso.hom.app s).hom ≫ (h.functor.inv.map (P.liftConeMorphism (h.functor.obj s))).hom) ≫
+        (h.unitIso.inv.app c).hom :=
   rfl
 #align category_theory.limits.is_limit.of_cone_equiv_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc
 
@@ -268,7 +268,7 @@ theorem ofConeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
 theorem ofConeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
     (h : Cone G ≌ Cone F) {c : Cone G} (P : IsLimit c) (s) :
     ((ofConeEquiv h).symm P).lift s =
-      (h.counitIso.inv.app s).Hom ≫ (h.functor.map (P.liftConeMorphism (h.inverse.obj s))).Hom :=
+      (h.counitIso.inv.app s).hom ≫ (h.functor.map (P.liftConeMorphism (h.inverse.obj s))).hom :=
   rfl
 #align category_theory.limits.is_limit.of_cone_equiv_symm_apply_desc CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc
 
@@ -458,8 +458,8 @@ def isoUniqueConeMorphism {t : Cone F} : IsLimit t ≅ ∀ s, Unique (s ⟶ t) w
     { default := h.liftConeMorphism s
       uniq := fun _ => h.uniq_cone_morphism }
   inv h :=
-    { lift := fun s => (h s).default.Hom
-      uniq := fun s f w => congrArg ConeMorphism.Hom ((h s).uniq ⟨f, w⟩) }
+    { lift := fun s => (h s).default.hom
+      uniq := fun s f w => congrArg ConeMorphism.hom ((h s).uniq ⟨f, w⟩) }
 #align category_theory.limits.is_limit.iso_unique_cone_morphism CategoryTheory.Limits.IsLimit.isoUniqueConeMorphism
 
 namespace OfNatIso
@@ -597,7 +597,7 @@ theorem desc_self {t : Cocone F} (h : IsColimit t) : h.desc t = 𝟙 t.pt :=
 -- Repackaging the definition in terms of cocone morphisms.
 /-- The universal morphism from a colimit cocone to any other cocone. -/
 @[simps]
-def descCoconeMorphism {t : Cocone F} (h : IsColimit t) (s : Cocone F) : t ⟶ s where Hom := h.desc s
+def descCoconeMorphism {t : Cocone F} (h : IsColimit t) (s : Cocone F) : t ⟶ s where hom := h.desc s
 #align category_theory.limits.is_colimit.desc_cocone_morphism CategoryTheory.Limits.IsColimit.descCoconeMorphism
 
 theorem uniq_cocone_morphism {s t : Cocone F} (h : IsColimit t) {f f' : t ⟶ s} : f = f' :=
@@ -627,10 +627,10 @@ and separately the factorisation condition.
 def mkCoconeMorphism {t : Cocone F} (desc : ∀ s : Cocone F, t ⟶ s)
     (uniq' : ∀ (s : Cocone F) (m : t ⟶ s), m = desc s) : IsColimit t
     where
-  desc s := (desc s).Hom
+  desc s := (desc s).hom
   uniq s m w :=
     have : CoconeMorphism.mk m w = desc s := by apply uniq'
-    congrArg CoconeMorphism.Hom this
+    congrArg CoconeMorphism.hom this
 #align category_theory.limits.is_colimit.mk_cocone_morphism CategoryTheory.Limits.IsColimit.mkCoconeMorphism
 
 /-- Colimit cocones on `F` are unique up to isomorphism. -/
@@ -685,7 +685,7 @@ def ofIsoColimit {r t : Cocone F} (P : IsColimit r) (i : r ≅ t) : IsColimit t
 
 @[simp]
 theorem ofIsoColimit_desc {r t : Cocone F} (P : IsColimit r) (i : r ≅ t) (s) :
-    (P.ofIsoColimit i).desc s = i.inv.Hom ≫ P.desc s :=
+    (P.ofIsoColimit i).desc s = i.inv.hom ≫ P.desc s :=
   rfl
 #align category_theory.limits.is_colimit.of_iso_colimit_desc CategoryTheory.Limits.IsColimit.ofIsoColimit_desc
 
@@ -714,7 +714,7 @@ first cocone was colimiting also.
 -/
 def ofPointIso {r t : Cocone F} (P : IsColimit r) [i : IsIso (P.desc t)] : IsColimit t :=
   ofIsoColimit P (by
-    haveI : IsIso (P.descCoconeMorphism t).Hom := i
+    haveI : IsIso (P.descCoconeMorphism t).hom := i
     haveI : IsIso (P.descCoconeMorphism t) := Cocones.cocone_iso_of_hom_iso _
     apply asIso (P.descCoconeMorphism t))
 #align category_theory.limits.is_colimit.of_point_iso CategoryTheory.Limits.IsColimit.ofPointIso
@@ -769,8 +769,8 @@ def ofCoconeEquiv {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D} (h : Cocone
 theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
     (h : Cocone G ≌ Cocone F) {c : Cocone G} (P : IsColimit (h.functor.obj c)) (s) :
     (ofCoconeEquiv h P).desc s =
-      (h.unit.app c).Hom ≫
-        (h.inverse.map (P.descCoconeMorphism (h.functor.obj s))).Hom ≫ (h.unitInv.app s).Hom :=
+      (h.unit.app c).hom ≫
+        (h.inverse.map (P.descCoconeMorphism (h.functor.obj s))).hom ≫ (h.unitInv.app s).hom :=
   rfl
 #align category_theory.limits.is_colimit.of_cocone_equiv_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc
 
@@ -778,7 +778,7 @@ theorem ofCoconeEquiv_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤
 theorem ofCoconeEquiv_symm_apply_desc {D : Type u₄} [Category.{v₄} D] {G : K ⥤ D}
     (h : Cocone G ≌ Cocone F) {c : Cocone G} (P : IsColimit c) (s) :
     ((ofCoconeEquiv h).symm P).desc s =
-      (h.functor.map (P.descCoconeMorphism (h.inverse.obj s))).Hom ≫ (h.counit.app s).Hom :=
+      (h.functor.map (P.descCoconeMorphism (h.inverse.obj s))).hom ≫ (h.counit.app s).hom :=
   rfl
 #align category_theory.limits.is_colimit.of_cocone_equiv_symm_apply_desc CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc
 
@@ -972,8 +972,8 @@ def isoUniqueCoconeMorphism {t : Cocone F} : IsColimit t ≅ ∀ s, Unique (t 
     { default := h.descCoconeMorphism s
       uniq := fun _ => h.uniq_cocone_morphism }
   inv h :=
-    { desc := fun s => (h s).default.Hom
-      uniq := fun s f w => congrArg CoconeMorphism.Hom ((h s).uniq ⟨f, w⟩) }
+    { desc := fun s => (h s).default.hom
+      uniq := fun s f w => congrArg CoconeMorphism.hom ((h s).uniq ⟨f, w⟩) }
 #align category_theory.limits.is_colimit.iso_unique_cocone_morphism CategoryTheory.Limits.IsColimit.isoUniqueCoconeMorphism
 
 namespace OfNatIso

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Mario Carneiro, Scott Morrison, Floris van Doorn
-
-! This file was ported from Lean 3 source module category_theory.limits.is_limit
-! leanprover-community/mathlib commit 740acc0e6f9adf4423f92a485d0456fc271482da
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Adjunction.Basic
 import Mathlib.CategoryTheory.Limits.Cones
 
+#align_import category_theory.limits.is_limit from "leanprover-community/mathlib"@"740acc0e6f9adf4423f92a485d0456fc271482da"
+
 /-!
 # Limits and colimits
 

@@ -394,6 +394,7 @@ end Equivalence
 
 /-- The universal property of a limit cone: a map `W ⟶ X` is the same as
   a cone on `F` with cone point `W`. -/
+@[pp_dot]
 def homIso (h : IsLimit t) (W : C) : ULift.{u₁} (W ⟶ t.pt : Type v₃) ≅ (const J).obj W ⟶ F where
   hom f := (t.extend f.down).π
   inv π := ⟨h.lift { pt := W, π }⟩
@@ -402,8 +403,6 @@ def homIso (h : IsLimit t) (W : C) : ULift.{u₁} (W ⟶ t.pt : Type v₃) ≅ (
     apply h.hom_ext; intro j; simp
 #align category_theory.limits.is_limit.hom_iso CategoryTheory.Limits.IsLimit.homIso
 
-pp_extended_field_notation IsLimit.homIso
-
 @[simp]
 theorem homIso_hom (h : IsLimit t) {W : C} (f : ULift.{u₁} (W ⟶ t.pt)) :
     (IsLimit.homIso h W).hom f = (t.extend f.down).π :=
@@ -417,8 +416,8 @@ def natIso (h : IsLimit t) : yoneda.obj t.pt ⋙ uliftFunctor.{u₁} ≅ F.cones
 #align category_theory.limits.is_limit.nat_iso CategoryTheory.Limits.IsLimit.natIso
 
 /-- Another, more explicit, formulation of the universal property of a limit cone.
-See also `homIso`.
--/
+See also `homIso`. -/
+@[pp_dot]
 def homIso' (h : IsLimit t) (W : C) :
     ULift.{u₁} (W ⟶ t.pt : Type v₃) ≅
       { p : ∀ j, W ⟶ F.obj j // ∀ {j j'} (f : j ⟶ j'), p j ≫ F.map f = p j' } :=
@@ -430,8 +429,6 @@ def homIso' (h : IsLimit t) (W : C) :
           naturality := fun j j' f => by dsimp; rw [id_comp]; exact (p.2 f).symm } }
 #align category_theory.limits.is_limit.hom_iso' CategoryTheory.Limits.IsLimit.homIso'
 
-pp_extended_field_notation IsLimit.homIso'
-
 /-- If G : C → D is a faithful functor which sends t to a limit cone,
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/
@@ -909,6 +906,7 @@ end Equivalence
 
 /-- The universal property of a colimit cocone: a map `X ⟶ W` is the same as
   a cocone on `F` with cone point `W`. -/
+@[pp_dot]
 def homIso (h : IsColimit t) (W : C) : ULift.{u₁} (t.pt ⟶ W : Type v₃) ≅ F ⟶ (const J).obj W where
   hom f := (t.extend f.down).ι
   inv ι := ⟨h.desc
@@ -919,8 +917,6 @@ def homIso (h : IsColimit t) (W : C) : ULift.{u₁} (t.pt ⟶ W : Type v₃) ≅
     apply h.hom_ext; intro j; simp
 #align category_theory.limits.is_colimit.hom_iso CategoryTheory.Limits.IsColimit.homIso
 
-pp_extended_field_notation IsColimit.homIso
-
 @[simp]
 theorem homIso_hom (h : IsColimit t) {W : C} (f : ULift (t.pt ⟶ W)) :
     (IsColimit.homIso h W).hom f = (t.extend f.down).ι :=
@@ -934,8 +930,8 @@ def natIso (h : IsColimit t) : coyoneda.obj (op t.pt) ⋙ uliftFunctor.{u₁} 
 #align category_theory.limits.is_colimit.nat_iso CategoryTheory.Limits.IsColimit.natIso
 
 /-- Another, more explicit, formulation of the universal property of a colimit cocone.
-See also `homIso`.
--/
+See also `homIso`. -/
+@[pp_dot]
 def homIso' (h : IsColimit t) (W : C) :
     ULift.{u₁} (t.pt ⟶ W : Type v₃) ≅
       { p : ∀ j, F.obj j ⟶ W // ∀ {j j' : J} (f : j ⟶ j'), F.map f ≫ p j' = p j } :=
@@ -947,8 +943,6 @@ def homIso' (h : IsColimit t) (W : C) :
           naturality := fun j j' f => by dsimp; rw [comp_id]; exact p.2 f } }
 #align category_theory.limits.is_colimit.hom_iso' CategoryTheory.Limits.IsColimit.homIso'
 
-pp_extended_field_notation IsColimit.homIso'
-
 /-- If G : C → D is a faithful functor which sends t to a colimit cocone,
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -77,7 +77,7 @@ attribute [reassoc (attr := simp)] IsLimit.fac
 namespace IsLimit
 
 instance subsingleton {t : Cone F} : Subsingleton (IsLimit t) :=
-  ⟨by intro P Q ; cases P ; cases Q ; congr ; aesop_cat⟩
+  ⟨by intro P Q; cases P; cases Q; congr; aesop_cat⟩
 #align category_theory.limits.is_limit.subsingleton CategoryTheory.Limits.IsLimit.subsingleton
 
 /-- Given a natural transformation `α : F ⟶ G`, we give a morphism from the cone point
@@ -580,7 +580,7 @@ attribute [-simp, nolint simpNF] IsColimit.mk.injEq
 namespace IsColimit
 
 instance subsingleton {t : Cocone F} : Subsingleton (IsColimit t) :=
-  ⟨by intro P Q ; cases P ; cases Q ; congr ; aesop_cat⟩
+  ⟨by intro P Q; cases P; cases Q; congr; aesop_cat⟩
 #align category_theory.limits.is_colimit.subsingleton CategoryTheory.Limits.IsColimit.subsingleton
 
 /-- Given a natural transformation `α : F ⟶ G`, we give a morphism from the cocone point
@@ -956,7 +956,7 @@ def ofFaithful {t : Cocone F} {D : Type u₄} [Category.{v₄} D] (G : C ⥤ D)
     (ht : IsColimit (mapCocone G t)) (desc : ∀ s : Cocone F, t.pt ⟶ s.pt)
     (h : ∀ s, G.map (desc s) = ht.desc (mapCocone G s)) : IsColimit t :=
   { desc
-    fac := fun s j => by apply G.map_injective ; rw [G.map_comp, h] ; apply ht.fac
+    fac := fun s j => by apply G.map_injective; rw [G.map_comp, h]; apply ht.fac
     uniq := fun s m w => by
       apply G.map_injective; rw [h]
       refine' ht.uniq (mapCocone G s) _ fun j => _
@@ -1005,7 +1005,7 @@ def homOfCocone (s : Cocone F) : X ⟶ s.pt :=
 theorem coconeOfHom_homOfCocone (s : Cocone F) : coconeOfHom h (homOfCocone h s) = s := by
   dsimp [coconeOfHom, homOfCocone];
   have ⟨s_pt,s_ι⟩ := s
-  congr ; dsimp
+  congr; dsimp
   convert congrFun (congrFun (congrArg NatTrans.app h.inv_hom_id) s_pt) s_ι using 1
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_of_cocone CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_homOfCocone
 

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -997,7 +997,7 @@ def coconeOfHom {Y : C} (f : X ⟶ Y) : Cocone F where
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom
 
 /-- If `F.cocones` is corepresented by `X`, each cocone `s` gives a morphism `X ⟶ s.pt`. -/
-def homOfCocone (s : Cocone F) : X ⟶ s.pt:=
+def homOfCocone (s : Cocone F) : X ⟶ s.pt :=
   (h.inv.app s.pt s.ι).down
 #align category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone
 

Clean up of automation in the category theory library. Leaving out unnecessary proof steps, or fields done by aesop_cat, and making more use of available autoparameters.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

@@ -77,7 +77,7 @@ attribute [reassoc (attr := simp)] IsLimit.fac
 namespace IsLimit
 
 instance subsingleton {t : Cone F} : Subsingleton (IsLimit t) :=
-  ⟨by intro P Q ; cases P ; cases Q ; congr ; ext ; aesop_cat⟩
+  ⟨by intro P Q ; cases P ; cases Q ; congr ; aesop_cat⟩
 #align category_theory.limits.is_limit.subsingleton CategoryTheory.Limits.IsLimit.subsingleton
 
 /-- Given a natural transformation `α : F ⟶ G`, we give a morphism from the cone point
@@ -192,8 +192,7 @@ theorem ofIsoLimit_lift {r t : Cone F} (P : IsLimit r) (i : r ≅ t) (s) :
 #align category_theory.limits.is_limit.of_iso_limit_lift CategoryTheory.Limits.IsLimit.ofIsoLimit_lift
 
 /-- Isomorphism of cones preserves whether or not they are limiting cones. -/
-def equivIsoLimit {r t : Cone F} (i : r ≅ t) : IsLimit r ≃ IsLimit t
-    where
+def equivIsoLimit {r t : Cone F} (i : r ≅ t) : IsLimit r ≃ IsLimit t where
   toFun h := h.ofIsoLimit i
   invFun h := h.ofIsoLimit i.symm
   left_inv := by aesop_cat
@@ -216,12 +215,11 @@ theorem equivIsoLimit_symm_apply {r t : Cone F} (i : r ≅ t) (P : IsLimit t) :
 first cone was limiting also.
 -/
 def ofPointIso {r t : Cone F} (P : IsLimit r) [i : IsIso (P.lift t)] : IsLimit t :=
-  ofIsoLimit P
-    (by
-      haveI : IsIso (P.liftConeMorphism t).Hom := i
-      haveI : IsIso (P.liftConeMorphism t) := Cones.cone_iso_of_hom_iso _
-      symm
-      apply asIso (P.liftConeMorphism t))
+  ofIsoLimit P (by
+    haveI : IsIso (P.liftConeMorphism t).Hom := i
+    haveI : IsIso (P.liftConeMorphism t) := Cones.cone_iso_of_hom_iso _
+    symm
+    apply asIso (P.liftConeMorphism t))
 #align category_theory.limits.is_limit.of_point_iso CategoryTheory.Limits.IsLimit.ofPointIso
 
 variable {t : Cone F}
@@ -235,7 +233,8 @@ theorem hom_lift (h : IsLimit t) {W : C} (m : W ⟶ t.pt) :
   each cone morphism are equal. -/
 theorem hom_ext (h : IsLimit t) {W : C} {f f' : W ⟶ t.pt}
     (w : ∀ j, f ≫ t.π.app j = f' ≫ t.π.app j) :
-    f = f' := by rw [h.hom_lift f, h.hom_lift f']; congr; exact funext w
+    f = f' := by
+  rw [h.hom_lift f, h.hom_lift f']; congr; exact funext w
 #align category_theory.limits.is_limit.hom_ext CategoryTheory.Limits.IsLimit.hom_ext
 
 /-- Given a right adjoint functor between categories of cones,
@@ -401,8 +400,6 @@ def homIso (h : IsLimit t) (W : C) : ULift.{u₁} (W ⟶ t.pt : Type v₃) ≅ (
   hom_inv_id := by
     funext f; apply ULift.ext
     apply h.hom_ext; intro j; simp
-  inv_hom_id := by
-    funext f; dsimp [const]; aesop_cat
 #align category_theory.limits.is_limit.hom_iso CategoryTheory.Limits.IsLimit.homIso
 
 pp_extended_field_notation IsLimit.homIso
@@ -415,12 +412,8 @@ theorem homIso_hom (h : IsLimit t) {W : C} (f : ULift.{u₁} (W ⟶ t.pt)) :
 
 /-- The limit of `F` represents the functor taking `W` to
   the set of cones on `F` with cone point `W`. -/
-def natIso (h : IsLimit t) : yoneda.obj t.pt ⋙ uliftFunctor.{u₁} ≅ F.cones := by
-  refine NatIso.ofComponents (fun W => IsLimit.homIso h (unop W)) ?_
-  intro X Y f
-  dsimp [yoneda,homIso,const,uliftFunctor,cones]
-  funext g
-  aesop_cat
+def natIso (h : IsLimit t) : yoneda.obj t.pt ⋙ uliftFunctor.{u₁} ≅ F.cones :=
+  NatIso.ofComponents fun W => IsLimit.homIso h (unop W)
 #align category_theory.limits.is_limit.nat_iso CategoryTheory.Limits.IsLimit.natIso
 
 /-- Another, more explicit, formulation of the universal property of a limit cone.
@@ -587,7 +580,7 @@ attribute [-simp, nolint simpNF] IsColimit.mk.injEq
 namespace IsColimit
 
 instance subsingleton {t : Cocone F} : Subsingleton (IsColimit t) :=
-  ⟨by intro P Q ; cases P ; cases Q ; congr ; ext ; aesop_cat⟩
+  ⟨by intro P Q ; cases P ; cases Q ; congr ; aesop_cat⟩
 #align category_theory.limits.is_colimit.subsingleton CategoryTheory.Limits.IsColimit.subsingleton
 
 /-- Given a natural transformation `α : F ⟶ G`, we give a morphism from the cocone point
@@ -703,8 +696,7 @@ theorem ofIsoColimit_desc {r t : Cocone F} (P : IsColimit r) (i : r ≅ t) (s) :
 #align category_theory.limits.is_colimit.of_iso_colimit_desc CategoryTheory.Limits.IsColimit.ofIsoColimit_desc
 
 /-- Isomorphism of cocones preserves whether or not they are colimiting cocones. -/
-def equivIsoColimit {r t : Cocone F} (i : r ≅ t) : IsColimit r ≃ IsColimit t
-    where
+def equivIsoColimit {r t : Cocone F} (i : r ≅ t) : IsColimit r ≃ IsColimit t where
   toFun h := h.ofIsoColimit i
   invFun h := h.ofIsoColimit i.symm
   left_inv := by aesop_cat
@@ -727,11 +719,10 @@ theorem equivIsoColimit_symm_apply {r t : Cocone F} (i : r ≅ t) (P : IsColimit
 first cocone was colimiting also.
 -/
 def ofPointIso {r t : Cocone F} (P : IsColimit r) [i : IsIso (P.desc t)] : IsColimit t :=
-  ofIsoColimit P
-    (by
-      haveI : IsIso (P.descCoconeMorphism t).Hom := i
-      haveI : IsIso (P.descCoconeMorphism t) := Cocones.cocone_iso_of_hom_iso _
-      apply asIso (P.descCoconeMorphism t))
+  ofIsoColimit P (by
+    haveI : IsIso (P.descCoconeMorphism t).Hom := i
+    haveI : IsIso (P.descCoconeMorphism t) := Cocones.cocone_iso_of_hom_iso _
+    apply asIso (P.descCoconeMorphism t))
 #align category_theory.limits.is_colimit.of_point_iso CategoryTheory.Limits.IsColimit.ofPointIso
 
 variable {t : Cocone F}
@@ -920,15 +911,12 @@ end Equivalence
   a cocone on `F` with cone point `W`. -/
 def homIso (h : IsColimit t) (W : C) : ULift.{u₁} (t.pt ⟶ W : Type v₃) ≅ F ⟶ (const J).obj W where
   hom f := (t.extend f.down).ι
-  inv ι :=
-    ⟨h.desc
-        { pt := W
-          ι }⟩
+  inv ι := ⟨h.desc
+      { pt := W
+        ι }⟩
   hom_inv_id := by
     funext f; apply ULift.ext
     apply h.hom_ext; intro j; simp
-  inv_hom_id := by
-    funext f; dsimp [const]; aesop_cat
 #align category_theory.limits.is_colimit.hom_iso CategoryTheory.Limits.IsColimit.homIso
 
 pp_extended_field_notation IsColimit.homIso
@@ -942,7 +930,7 @@ theorem homIso_hom (h : IsColimit t) {W : C} (f : ULift (t.pt ⟶ W)) :
 /-- The colimit of `F` represents the functor taking `W` to
   the set of cocones on `F` with cone point `W`. -/
 def natIso (h : IsColimit t) : coyoneda.obj (op t.pt) ⋙ uliftFunctor.{u₁} ≅ F.cocones :=
-  NatIso.ofComponents (IsColimit.homIso h) (by intros; funext; aesop_cat)
+  NatIso.ofComponents (IsColimit.homIso h)
 #align category_theory.limits.is_colimit.nat_iso CategoryTheory.Limits.IsColimit.natIso
 
 /-- Another, more explicit, formulation of the universal property of a colimit cocone.
@@ -1003,8 +991,7 @@ variable {X : C} (h : coyoneda.obj (op X) ⋙ uliftFunctor.{u₁} ≅ F.cocones)
 
 /-- If `F.cocones` is corepresented by `X`, each morphism `f : X ⟶ Y` gives a cocone with cone
 point `Y`. -/
-def coconeOfHom {Y : C} (f : X ⟶ Y) : Cocone F
-    where
+def coconeOfHom {Y : C} (f : X ⟶ Y) : Cocone F where
   pt := Y
   ι := h.hom.app Y ⟨f⟩
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom

Add some pp_extended_field_notation, for opt-in cases with additional arguments.

Co-authored-by: Kyle Miller <kmill31415@gmail.com>

@@ -405,6 +405,8 @@ def homIso (h : IsLimit t) (W : C) : ULift.{u₁} (W ⟶ t.pt : Type v₃) ≅ (
     funext f; dsimp [const]; aesop_cat
 #align category_theory.limits.is_limit.hom_iso CategoryTheory.Limits.IsLimit.homIso
 
+pp_extended_field_notation IsLimit.homIso
+
 @[simp]
 theorem homIso_hom (h : IsLimit t) {W : C} (f : ULift.{u₁} (W ⟶ t.pt)) :
     (IsLimit.homIso h W).hom f = (t.extend f.down).π :=
@@ -435,6 +437,8 @@ def homIso' (h : IsLimit t) (W : C) :
           naturality := fun j j' f => by dsimp; rw [id_comp]; exact (p.2 f).symm } }
 #align category_theory.limits.is_limit.hom_iso' CategoryTheory.Limits.IsLimit.homIso'
 
+pp_extended_field_notation IsLimit.homIso'
+
 /-- If G : C → D is a faithful functor which sends t to a limit cone,
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/
@@ -927,6 +931,8 @@ def homIso (h : IsColimit t) (W : C) : ULift.{u₁} (t.pt ⟶ W : Type v₃) ≅
     funext f; dsimp [const]; aesop_cat
 #align category_theory.limits.is_colimit.hom_iso CategoryTheory.Limits.IsColimit.homIso
 
+pp_extended_field_notation IsColimit.homIso
+
 @[simp]
 theorem homIso_hom (h : IsColimit t) {W : C} (f : ULift (t.pt ⟶ W)) :
     (IsColimit.homIso h W).hom f = (t.extend f.down).ι :=
@@ -953,6 +959,8 @@ def homIso' (h : IsColimit t) (W : C) :
           naturality := fun j j' f => by dsimp; rw [comp_id]; exact p.2 f } }
 #align category_theory.limits.is_colimit.hom_iso' CategoryTheory.Limits.IsColimit.homIso'
 
+pp_extended_field_notation IsColimit.homIso'
+
 /-- If G : C → D is a faithful functor which sends t to a colimit cocone,
   then it suffices to check that the induced maps for the image of t
   can be lifted to maps of C. -/

• There is now configuration for congr!, convert, and convert_to to control parts of the congruence algorithm, in particular transparency settings when applying congruence lemmas.
• congr! now applies congruence lemmas with reducible transparency by default. This prevents it from unfolding definitions when applying congruence lemmas. It also now tries both the LHS-biased and RHS-biased simp congruence lemmas, with a configuration option to set which it should try first.
• There is now a new HEq congruence lemma generator that gives each hypothesis access to the proofs of previous hypotheses. This means that if you have an equality ⊢ ⟨a, x⟩ = ⟨b, y⟩ of sigma types, congr! turns this into goals ⊢ a = b and ⊢ a = b → HEq x y (note that congr! will also auto-introduce a = b for you in the second goal). This congruence lemma generator applies to more cases than the simp congruence lemma generator does.
• congr! (and hence convert) are more careful about applying lemmas that don't force definitions to unfold. There were a number of cases in mathlib where the implementation of congr was being abused to unfold definitions.
• With set_option trace.congr! true you can see what congr! sees when it is deciding on congruence lemmas.
• There is also a bug fix in convert_to to do using 1 when there is no using clause, to match its documentation.

Note that congr! is more capable than congr at finding a way to equate left-hand sides and right-hand sides, so you will frequently need to limit its depth with a using clause. However, there is also a new heuristic to prevent considering unlikely-to-be-provable type equalities (controlled by the typeEqs option), which can help limit the depth automatically.

There is also a predefined configuration that you can invoke with, for example, convert (config := .unfoldSameFun) h, that causes it to behave more like congr, including using default transparency when unfolding.

@@ -492,8 +492,8 @@ theorem coneOfHom_homOfCone (s : Cone F) : coneOfHom h (homOfCone h s) = s := by
   dsimp [coneOfHom, homOfCone]
   match s with
   | .mk s_pt s_π =>
-    congr ; dsimp
-    convert congrFun (congrFun (congrArg NatTrans.app h.inv_hom_id) (op s_pt)) s_π
+    congr; dsimp
+    convert congrFun (congrFun (congrArg NatTrans.app h.inv_hom_id) (op s_pt)) s_π using 1
 #align category_theory.limits.is_limit.of_nat_iso.cone_of_hom_of_cone CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_homOfCone
 
 @[simp]
@@ -1011,7 +1011,7 @@ theorem coconeOfHom_homOfCocone (s : Cocone F) : coconeOfHom h (homOfCocone h s)
   dsimp [coconeOfHom, homOfCocone];
   have ⟨s_pt,s_ι⟩ := s
   congr ; dsimp
-  convert congrFun (congrFun (congrArg NatTrans.app h.inv_hom_id) s_pt) s_ι
+  convert congrFun (congrFun (congrArg NatTrans.app h.inv_hom_id) s_pt) s_ι using 1
 #align category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_of_cocone CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_homOfCocone
 
 @[simp]

This commit makes aesop_cat and aesop_graph terminal (i.e. they either solve the goal or fail). This appears to solve issues where non-terminal tactics, when used as auto-params, introduce unknown universe variables. See

https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Goal.20state.20not.20updating.2C.20bugs.2C.20etc.2E

Since there are some intended nonterminal uses of aesop_cat, we introduce aesop_cat_nonterminal as the nonterminal equivalent of aesop_cat.

@@ -610,7 +610,8 @@ def descCoconeMorphism {t : Cocone F} (h : IsColimit t) (s : Cocone F) : t ⟶ s
 #align category_theory.limits.is_colimit.desc_cocone_morphism CategoryTheory.Limits.IsColimit.descCoconeMorphism
 
 theorem uniq_cocone_morphism {s t : Cocone F} (h : IsColimit t) {f f' : t ⟶ s} : f = f' :=
-  have : ∀ {g : t ⟶ s}, g = h.descCoconeMorphism s := by intro g; aesop_cat; exact h.uniq _ _ g.w
+  have : ∀ {g : t ⟶ s}, g = h.descCoconeMorphism s := by
+    intro g; aesop_cat_nonterminal; exact h.uniq _ _ g.w
   this.trans this.symm
 #align category_theory.limits.is_colimit.uniq_cocone_morphism CategoryTheory.Limits.IsColimit.uniq_cocone_morphism
 

vscode is already configured by .vscode/settings.json to trim these on save. It's not clear how they've managed to stick around.

By doing this all in one PR now, it avoids getting random whitespace diffs in PRs later.

This was done with a regex search in vscode,

@@ -103,7 +103,7 @@ def liftConeMorphism {t : Cone F} (h : IsLimit t) (s : Cone F) : s ⟶ t where H
 #align category_theory.limits.is_limit.lift_cone_morphism CategoryTheory.Limits.IsLimit.liftConeMorphism
 
 theorem uniq_cone_morphism {s t : Cone F} (h : IsLimit t) {f f' : s ⟶ t} : f = f' :=
-  have : ∀ {g : s ⟶ t}, g = h.liftConeMorphism s := by 
+  have : ∀ {g : s ⟶ t}, g = h.liftConeMorphism s := by
     intro g; apply ConeMorphism.ext; exact h.uniq _ _ g.w
   this.trans this.symm
 #align category_theory.limits.is_limit.uniq_cone_morphism CategoryTheory.Limits.IsLimit.uniq_cone_morphism
@@ -233,7 +233,7 @@ theorem hom_lift (h : IsLimit t) {W : C} (m : W ⟶ t.pt) :
 
 /-- Two morphisms into a limit are equal if their compositions with
   each cone morphism are equal. -/
-theorem hom_ext (h : IsLimit t) {W : C} {f f' : W ⟶ t.pt} 
+theorem hom_ext (h : IsLimit t) {W : C} {f f' : W ⟶ t.pt}
     (w : ∀ j, f ≫ t.π.app j = f' ≫ t.π.app j) :
     f = f' := by rw [h.hom_lift f, h.hom_lift f']; congr; exact funext w
 #align category_theory.limits.is_limit.hom_ext CategoryTheory.Limits.IsLimit.hom_ext
@@ -382,7 +382,7 @@ def conePointsIsoOfEquivalence {F : J ⥤ C} {s : Cone F} {G : K ⥤ C} {t : Con
       simp only [Limits.Cone.whisker_π, Limits.Cones.postcompose_obj_π, fac, whiskerLeft_app,
         assoc, id_comp, invFunIdAssoc_hom_app, fac_assoc, NatTrans.comp_app]
       rw [counit_app_functor, ←Functor.comp_map]
-      have l : 
+      have l :
         NatTrans.app w.hom j = NatTrans.app w.hom (Prefunctor.obj (𝟭 J).toPrefunctor j) := by dsimp
       rw [l,w.hom.naturality]
       simp
@@ -398,10 +398,10 @@ end Equivalence
 def homIso (h : IsLimit t) (W : C) : ULift.{u₁} (W ⟶ t.pt : Type v₃) ≅ (const J).obj W ⟶ F where
   hom f := (t.extend f.down).π
   inv π := ⟨h.lift { pt := W, π }⟩
-  hom_inv_id := by 
+  hom_inv_id := by
     funext f; apply ULift.ext
     apply h.hom_ext; intro j; simp
-  inv_hom_id := by 
+  inv_hom_id := by
     funext f; dsimp [const]; aesop_cat
 #align category_theory.limits.is_limit.hom_iso CategoryTheory.Limits.IsLimit.homIso
 
@@ -415,9 +415,9 @@ theorem homIso_hom (h : IsLimit t) {W : C} (f : ULift.{u₁} (W ⟶ t.pt)) :
   the set of cones on `F` with cone point `W`. -/
 def natIso (h : IsLimit t) : yoneda.obj t.pt ⋙ uliftFunctor.{u₁} ≅ F.cones := by
   refine NatIso.ofComponents (fun W => IsLimit.homIso h (unop W)) ?_
-  intro X Y f 
+  intro X Y f
   dsimp [yoneda,homIso,const,uliftFunctor,cones]
-  funext g 
+  funext g
   aesop_cat
 #align category_theory.limits.is_limit.nat_iso CategoryTheory.Limits.IsLimit.natIso
 
@@ -490,8 +490,8 @@ def homOfCone (s : Cone F) : s.pt ⟶ X :=
 @[simp]
 theorem coneOfHom_homOfCone (s : Cone F) : coneOfHom h (homOfCone h s) = s := by
   dsimp [coneOfHom, homOfCone]
-  match s with 
-  | .mk s_pt s_π => 
+  match s with
+  | .mk s_pt s_π =>
     congr ; dsimp
     convert congrFun (congrFun (congrArg NatTrans.app h.inv_hom_id) (op s_pt)) s_π
 #align category_theory.limits.is_limit.of_nat_iso.cone_of_hom_of_cone CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_homOfCone
@@ -919,10 +919,10 @@ def homIso (h : IsColimit t) (W : C) : ULift.{u₁} (t.pt ⟶ W : Type v₃) ≅
     ⟨h.desc
         { pt := W
           ι }⟩
-  hom_inv_id := by 
+  hom_inv_id := by
     funext f; apply ULift.ext
     apply h.hom_ext; intro j; simp
-  inv_hom_id := by 
+  inv_hom_id := by
     funext f; dsimp [const]; aesop_cat
 #align category_theory.limits.is_colimit.hom_iso CategoryTheory.Limits.IsColimit.homIso
 
@@ -1007,7 +1007,7 @@ def homOfCocone (s : Cocone F) : X ⟶ s.pt:=
 
 @[simp]
 theorem coconeOfHom_homOfCocone (s : Cocone F) : coconeOfHom h (homOfCocone h s) = s := by
-  dsimp [coconeOfHom, homOfCocone]; 
+  dsimp [coconeOfHom, homOfCocone];
   have ⟨s_pt,s_ι⟩ := s
   congr ; dsimp
   convert congrFun (congrFun (congrArg NatTrans.app h.inv_hom_id) s_pt) s_ι

@@ -1074,4 +1074,3 @@ end
 end IsColimit
 
 end CategoryTheory.Limits
-#lint