category_theory.structured_arrow | Mathlib porting status

(last sync)

chore(category_theory/comma): removed obviously tactic for data fields (#18440)

For some comma categories like structured_arrow, over, under, the definition of some data fields could be obtained automatically by the obviously tactic. This PR removes this behaviour. Instead, specialized constructors like structured_arrow.mk or structured_arrow.hom_mk are used more systematically.

Diff

@@ -69,7 +69,7 @@ structured arrow given by `(X ⟶ F(U)) ⟶ (X ⟶ F(U) ⟶ F(Y))`.
 -/
 def hom_mk' {F : C ⥤ D} {X : D} {Y : C}
 (U : structured_arrow X F) (f : U.right ⟶ Y) :
-U ⟶ mk (U.hom ≫ F.map f) := { right := f }
+U ⟶ mk (U.hom ≫ F.map f) := { left := eq_to_hom (by ext), right := f }
 
 /--
 To construct an isomorphism of structured arrows,
@@ -165,9 +165,9 @@ comma.pre_right _ F G
 /-- The functor `(S, F) ⥤ (G(S), F ⋙ G)`. -/
 @[simps] def post (S : C) (F : B ⥤ C) (G : C ⥤ D) :
   structured_arrow S F ⥤ structured_arrow (G.obj S) (F ⋙ G) :=
-{ obj := λ X, { right := X.right, hom := G.map X.hom },
-  map := λ X Y f, { right := f.right, w' :=
-    by { simp [functor.comp_map, ←G.map_comp, ← f.w] } } }
+{ obj := λ X, structured_arrow.mk (G.map X.hom),
+  map := λ X Y f, structured_arrow.hom_mk f.right
+    (by simp [functor.comp_map, ←G.map_comp, ← f.w]) }
 
 instance small_proj_preimage_of_locally_small {𝒢 : set C} [small.{v₁} 𝒢] [locally_small.{v₁} D] :
   small.{v₁} ((proj S T).obj ⁻¹' 𝒢) :=
@@ -315,9 +315,9 @@ comma.pre_left F G _
 /-- The functor `(F, S) ⥤ (F ⋙ G, G(S))`. -/
 @[simps] def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :
   costructured_arrow F S ⥤ costructured_arrow (F ⋙ G) (G.obj S) :=
-{ obj := λ X, { left := X.left, hom := G.map X.hom },
-  map := λ X Y f, { left := f.left, w' :=
-    by { simp [functor.comp_map, ←G.map_comp, ← f.w] } } }
+{ obj := λ X, costructured_arrow.mk (G.map X.hom),
+  map := λ X Y f, costructured_arrow.hom_mk f.left
+    (by simp [functor.comp_map, ←G.map_comp, ← f.w]), }
 
 instance small_proj_preimage_of_locally_small {𝒢 : set C} [small.{v₁} 𝒢] [locally_small.{v₁} D] :
   small.{v₁} ((proj S T).obj ⁻¹' 𝒢) :=

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-14-09

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

f736ea6b

Diff

@@ -141,7 +141,7 @@ theorem ext_iff {A B : StructuredArrow S T} (f g : A ⟶ B) : f = g ↔ f.right
 -/
 
 #print CategoryTheory.StructuredArrow.proj_faithful /-
-instance proj_faithful : Faithful (proj S T) where map_injective' X Y := ext
+instance proj_faithful : CategoryTheory.Functor.Faithful (proj S T) where map_injective' X Y := ext
 #align category_theory.structured_arrow.proj_faithful CategoryTheory.StructuredArrow.proj_faithful
 -/
 
@@ -223,7 +223,7 @@ theorem map_comp {f : S ⟶ S'} {f' : S' ⟶ S''} {h : StructuredArrow S'' T} :
 -/
 
 #print CategoryTheory.StructuredArrow.proj_reflectsIsomorphisms /-
-instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T)
+instance proj_reflectsIsomorphisms : CategoryTheory.Functor.ReflectsIsomorphisms (proj S T)
     where reflects Y Z f t :=
     ⟨⟨structured_arrow.hom_mk (inv ((proj S T).map f)) (by simp), by tidy⟩⟩
 #align category_theory.structured_arrow.proj_reflects_iso CategoryTheory.StructuredArrow.proj_reflectsIsomorphisms
@@ -235,7 +235,8 @@ attribute [local tidy] tactic.discrete_cases
 
 #print CategoryTheory.StructuredArrow.mkIdInitial /-
 /-- The identity structured arrow is initial. -/
-def mkIdInitial [Full T] [Faithful T] : IsInitial (mk (𝟙 (T.obj Y)))
+def mkIdInitial [CategoryTheory.Functor.Full T] [CategoryTheory.Functor.Faithful T] :
+    IsInitial (mk (𝟙 (T.obj Y)))
     where
   desc c := homMk (T.preimage c.pt.Hom) (by dsimp; simp)
   uniq c m _ := by
@@ -374,7 +375,7 @@ theorem ext_iff {A B : CostructuredArrow S T} (f g : A ⟶ B) : f = g ↔ f.left
 -/
 
 #print CategoryTheory.CostructuredArrow.proj_faithful /-
-instance proj_faithful : Faithful (proj S T) where map_injective' X Y := ext
+instance proj_faithful : CategoryTheory.Functor.Faithful (proj S T) where map_injective' X Y := ext
 #align category_theory.costructured_arrow.proj_faithful CategoryTheory.CostructuredArrow.proj_faithful
 -/
 
@@ -456,7 +457,7 @@ theorem map_comp {f : T ⟶ T'} {f' : T' ⟶ T''} {h : CostructuredArrow S T} :
 -/
 
 #print CategoryTheory.CostructuredArrow.proj_reflectsIsomorphisms /-
-instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T)
+instance proj_reflectsIsomorphisms : CategoryTheory.Functor.ReflectsIsomorphisms (proj S T)
     where reflects Y Z f t :=
     ⟨⟨costructured_arrow.hom_mk (inv ((proj S T).map f)) (by simp), by tidy⟩⟩
 #align category_theory.costructured_arrow.proj_reflects_iso CategoryTheory.CostructuredArrow.proj_reflectsIsomorphisms
@@ -468,7 +469,8 @@ attribute [local tidy] tactic.discrete_cases
 
 #print CategoryTheory.CostructuredArrow.mkIdTerminal /-
 /-- The identity costructured arrow is terminal. -/
-def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y)))
+def mkIdTerminal [CategoryTheory.Functor.Full S] [CategoryTheory.Functor.Faithful S] :
+    IsTerminal (mk (𝟙 (S.obj Y)))
     where
   lift c := homMk (S.preimage c.pt.Hom) (by dsimp; simp)
   uniq := by

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz, Scott Morrison
 -/
-import CategoryTheory.Punit
-import CategoryTheory.Comma
+import CategoryTheory.PUnit
+import CategoryTheory.Comma.Basic
 import CategoryTheory.Limits.Shapes.Terminal
 import CategoryTheory.EssentiallySmall

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz, Scott Morrison
 -/
-import Mathbin.CategoryTheory.Punit
-import Mathbin.CategoryTheory.Comma
-import Mathbin.CategoryTheory.Limits.Shapes.Terminal
-import Mathbin.CategoryTheory.EssentiallySmall
+import CategoryTheory.Punit
+import CategoryTheory.Comma
+import CategoryTheory.Limits.Shapes.Terminal
+import CategoryTheory.EssentiallySmall
 
 #align_import category_theory.structured_arrow from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.structured_arrow
-! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Punit
 import Mathbin.CategoryTheory.Comma
 import Mathbin.CategoryTheory.Limits.Shapes.Terminal
 import Mathbin.CategoryTheory.EssentiallySmall
 
+#align_import category_theory.structured_arrow from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
 /-!
 # The category of "structured arrows"

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -59,31 +59,42 @@ def proj (S : D) (T : C ⥤ D) : StructuredArrow S T ⥤ C :=
 
 variable {S S' S'' : D} {Y Y' : C} {T : C ⥤ D}
 
+#print CategoryTheory.StructuredArrow.mk /-
 /-- Construct a structured arrow from a morphism. -/
 def mk (f : S ⟶ T.obj Y) : StructuredArrow S T :=
   ⟨⟨⟨⟩⟩, Y, f⟩
 #align category_theory.structured_arrow.mk CategoryTheory.StructuredArrow.mk
+-/
 
+#print CategoryTheory.StructuredArrow.mk_left /-
 @[simp]
 theorem mk_left (f : S ⟶ T.obj Y) : (mk f).left = ⟨⟨⟩⟩ :=
   rfl
 #align category_theory.structured_arrow.mk_left CategoryTheory.StructuredArrow.mk_left
+-/
 
+#print CategoryTheory.StructuredArrow.mk_right /-
 @[simp]
 theorem mk_right (f : S ⟶ T.obj Y) : (mk f).right = Y :=
   rfl
 #align category_theory.structured_arrow.mk_right CategoryTheory.StructuredArrow.mk_right
+-/
 
+#print CategoryTheory.StructuredArrow.mk_hom_eq_self /-
 @[simp]
 theorem mk_hom_eq_self (f : S ⟶ T.obj Y) : (mk f).Hom = f :=
   rfl
 #align category_theory.structured_arrow.mk_hom_eq_self CategoryTheory.StructuredArrow.mk_hom_eq_self
+-/
 
+#print CategoryTheory.StructuredArrow.w /-
 @[simp, reassoc]
 theorem w {A B : StructuredArrow S T} (f : A ⟶ B) : A.Hom ≫ T.map f.right = B.Hom := by
   have := f.w <;> tidy
 #align category_theory.structured_arrow.w CategoryTheory.StructuredArrow.w
+-/
 
+#print CategoryTheory.StructuredArrow.homMk /-
 /-- To construct a morphism of structured arrows,
 we need a morphism of the objects underlying the target,
 and to check that the triangle commutes.
@@ -95,7 +106,9 @@ def homMk {f f' : StructuredArrow S T} (g : f.right ⟶ f'.right) (w : f.Hom ≫
   right := g
   w' := by dsimp; simpa using w.symm
 #align category_theory.structured_arrow.hom_mk CategoryTheory.StructuredArrow.homMk
+-/
 
+#print CategoryTheory.StructuredArrow.homMk' /-
 /-- Given a structured arrow `X ⟶ F(U)`, and an arrow `U ⟶ Y`, we can construct a morphism of
 structured arrow given by `(X ⟶ F(U)) ⟶ (X ⟶ F(U) ⟶ F(Y))`.
 -/
@@ -104,7 +117,9 @@ def homMk' {F : C ⥤ D} {X : D} {Y : C} (U : StructuredArrow X F) (f : U.right
   left := eqToHom (by ext)
   right := f
 #align category_theory.structured_arrow.hom_mk' CategoryTheory.StructuredArrow.homMk'
+-/
 
+#print CategoryTheory.StructuredArrow.isoMk /-
 /-- To construct an isomorphism of structured arrows,
 we need an isomorphism of the objects underlying the target,
 and to check that the triangle commutes.
@@ -114,6 +129,7 @@ def isoMk {f f' : StructuredArrow S T} (g : f.right ≅ f'.right) (w : f.Hom ≫
     f ≅ f' :=
   Comma.isoMk (eqToIso (by ext)) g (by simpa [eq_to_hom_map] using w.symm)
 #align category_theory.structured_arrow.iso_mk CategoryTheory.StructuredArrow.isoMk
+-/
 
 #print CategoryTheory.StructuredArrow.ext /-
 theorem ext {A B : StructuredArrow S T} (f g : A ⟶ B) : f.right = g.right → f = g :=
@@ -145,15 +161,19 @@ theorem epi_of_epi_right {A B : StructuredArrow S T} (f : A ⟶ B) [h : Epi f.ri
 #align category_theory.structured_arrow.epi_of_epi_right CategoryTheory.StructuredArrow.epi_of_epi_right
 -/
 
+#print CategoryTheory.StructuredArrow.mono_homMk /-
 instance mono_homMk {A B : StructuredArrow S T} (f : A.right ⟶ B.right) (w) [h : Mono f] :
     Mono (homMk f w) :=
   (proj S T).mono_of_mono_map h
 #align category_theory.structured_arrow.mono_hom_mk CategoryTheory.StructuredArrow.mono_homMk
+-/
 
+#print CategoryTheory.StructuredArrow.epi_homMk /-
 instance epi_homMk {A B : StructuredArrow S T} (f : A.right ⟶ B.right) (w) [h : Epi f] :
     Epi (homMk f w) :=
   (proj S T).epi_of_epi_map h
 #align category_theory.structured_arrow.epi_hom_mk CategoryTheory.StructuredArrow.epi_homMk
+-/
 
 #print CategoryTheory.StructuredArrow.eq_mk /-
 /-- Eta rule for structured arrows. Prefer `structured_arrow.eta`, since equality of objects tends
@@ -185,19 +205,25 @@ def map (f : S ⟶ S') : StructuredArrow S' T ⥤ StructuredArrow S T :=
 #align category_theory.structured_arrow.map CategoryTheory.StructuredArrow.map
 -/
 
+#print CategoryTheory.StructuredArrow.map_mk /-
 @[simp]
 theorem map_mk {f : S' ⟶ T.obj Y} (g : S ⟶ S') : (map g).obj (mk f) = mk (g ≫ f) :=
   rfl
 #align category_theory.structured_arrow.map_mk CategoryTheory.StructuredArrow.map_mk
+-/
 
+#print CategoryTheory.StructuredArrow.map_id /-
 @[simp]
 theorem map_id {f : StructuredArrow S T} : (map (𝟙 S)).obj f = f := by rw [eq_mk f]; simp
 #align category_theory.structured_arrow.map_id CategoryTheory.StructuredArrow.map_id
+-/
 
+#print CategoryTheory.StructuredArrow.map_comp /-
 @[simp]
 theorem map_comp {f : S ⟶ S'} {f' : S' ⟶ S''} {h : StructuredArrow S'' T} :
     (map (f ≫ f')).obj h = (map f).obj ((map f').obj h) := by rw [eq_mk h]; simp
 #align category_theory.structured_arrow.map_comp CategoryTheory.StructuredArrow.map_comp
+-/
 
 #print CategoryTheory.StructuredArrow.proj_reflectsIsomorphisms /-
 instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T)
@@ -210,6 +236,7 @@ open CategoryTheory.Limits
 
 attribute [local tidy] tactic.discrete_cases
 
+#print CategoryTheory.StructuredArrow.mkIdInitial /-
 /-- The identity structured arrow is initial. -/
 def mkIdInitial [Full T] [Faithful T] : IsInitial (mk (𝟙 (T.obj Y)))
     where
@@ -219,6 +246,7 @@ def mkIdInitial [Full T] [Faithful T] : IsInitial (mk (𝟙 (T.obj Y)))
     apply T.map_injective
     simpa only [hom_mk_right, T.image_preimage, ← w m] using (category.id_comp _).symm
 #align category_theory.structured_arrow.mk_id_initial CategoryTheory.StructuredArrow.mkIdInitial
+-/
 
 variable {A : Type u₃} [Category.{v₃} A] {B : Type u₄} [Category.{v₄} B]
 
@@ -230,6 +258,7 @@ def pre (S : D) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S (F ⋙ G) ⥤ St
 #align category_theory.structured_arrow.pre CategoryTheory.StructuredArrow.pre
 -/
 
+#print CategoryTheory.StructuredArrow.post /-
 /-- The functor `(S, F) ⥤ (G(S), F ⋙ G)`. -/
 @[simps]
 def post (S : C) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S F ⥤ StructuredArrow (G.obj S) (F ⋙ G)
@@ -237,7 +266,9 @@ def post (S : C) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S F ⥤ Structure
   obj X := StructuredArrow.mk (G.map X.Hom)
   map X Y f := StructuredArrow.homMk f.right (by simp [functor.comp_map, ← G.map_comp, ← f.w])
 #align category_theory.structured_arrow.post CategoryTheory.StructuredArrow.post
+-/
 
+#print CategoryTheory.StructuredArrow.small_proj_preimage_of_locallySmall /-
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) :=
   by
@@ -245,6 +276,7 @@ instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢]
     infer_instance
   exact Set.ext fun X => ⟨fun h => ⟨⟨⟨_, h⟩, X.Hom⟩, (eq_mk _).symm⟩, by tidy⟩
 #align category_theory.structured_arrow.small_proj_preimage_of_locally_small CategoryTheory.StructuredArrow.small_proj_preimage_of_locallySmall
+-/
 
 end StructuredArrow
 
@@ -272,30 +304,41 @@ def proj (S : C ⥤ D) (T : D) : CostructuredArrow S T ⥤ C :=
 
 variable {T T' T'' : D} {Y Y' : C} {S : C ⥤ D}
 
+#print CategoryTheory.CostructuredArrow.mk /-
 /-- Construct a costructured arrow from a morphism. -/
 def mk (f : S.obj Y ⟶ T) : CostructuredArrow S T :=
   ⟨Y, ⟨⟨⟩⟩, f⟩
 #align category_theory.costructured_arrow.mk CategoryTheory.CostructuredArrow.mk
+-/
 
+#print CategoryTheory.CostructuredArrow.mk_left /-
 @[simp]
 theorem mk_left (f : S.obj Y ⟶ T) : (mk f).left = Y :=
   rfl
 #align category_theory.costructured_arrow.mk_left CategoryTheory.CostructuredArrow.mk_left
+-/
 
+#print CategoryTheory.CostructuredArrow.mk_right /-
 @[simp]
 theorem mk_right (f : S.obj Y ⟶ T) : (mk f).right = ⟨⟨⟩⟩ :=
   rfl
 #align category_theory.costructured_arrow.mk_right CategoryTheory.CostructuredArrow.mk_right
+-/
 
+#print CategoryTheory.CostructuredArrow.mk_hom_eq_self /-
 @[simp]
 theorem mk_hom_eq_self (f : S.obj Y ⟶ T) : (mk f).Hom = f :=
   rfl
 #align category_theory.costructured_arrow.mk_hom_eq_self CategoryTheory.CostructuredArrow.mk_hom_eq_self
+-/
 
+#print CategoryTheory.CostructuredArrow.w /-
 @[simp, reassoc]
 theorem w {A B : CostructuredArrow S T} (f : A ⟶ B) : S.map f.left ≫ B.Hom = A.Hom := by tidy
 #align category_theory.costructured_arrow.w CategoryTheory.CostructuredArrow.w
+-/
 
+#print CategoryTheory.CostructuredArrow.homMk /-
 /-- To construct a morphism of costructured arrows,
 we need a morphism of the objects underlying the source,
 and to check that the triangle commutes.
@@ -307,7 +350,9 @@ def homMk {f f' : CostructuredArrow S T} (g : f.left ⟶ f'.left) (w : S.map g 
   right := eqToHom (by ext)
   w' := by simpa [eq_to_hom_map] using w
 #align category_theory.costructured_arrow.hom_mk CategoryTheory.CostructuredArrow.homMk
+-/
 
+#print CategoryTheory.CostructuredArrow.isoMk /-
 /-- To construct an isomorphism of costructured arrows,
 we need an isomorphism of the objects underlying the source,
 and to check that the triangle commutes.
@@ -317,6 +362,7 @@ def isoMk {f f' : CostructuredArrow S T} (g : f.left ≅ f'.left) (w : S.map g.H
     f ≅ f' :=
   Comma.isoMk g (eqToIso (by ext)) (by simpa [eq_to_hom_map] using w)
 #align category_theory.costructured_arrow.iso_mk CategoryTheory.CostructuredArrow.isoMk
+-/
 
 #print CategoryTheory.CostructuredArrow.ext /-
 theorem ext {A B : CostructuredArrow S T} (f g : A ⟶ B) (h : f.left = g.left) : f = g :=
@@ -348,15 +394,19 @@ theorem epi_of_epi_left {A B : CostructuredArrow S T} (f : A ⟶ B) [h : Epi f.l
 #align category_theory.costructured_arrow.epi_of_epi_left CategoryTheory.CostructuredArrow.epi_of_epi_left
 -/
 
+#print CategoryTheory.CostructuredArrow.mono_homMk /-
 instance mono_homMk {A B : CostructuredArrow S T} (f : A.left ⟶ B.left) (w) [h : Mono f] :
     Mono (homMk f w) :=
   (proj S T).mono_of_mono_map h
 #align category_theory.costructured_arrow.mono_hom_mk CategoryTheory.CostructuredArrow.mono_homMk
+-/
 
+#print CategoryTheory.CostructuredArrow.epi_homMk /-
 instance epi_homMk {A B : CostructuredArrow S T} (f : A.left ⟶ B.left) (w) [h : Epi f] :
     Epi (homMk f w) :=
   (proj S T).epi_of_epi_map h
 #align category_theory.costructured_arrow.epi_hom_mk CategoryTheory.CostructuredArrow.epi_homMk
+-/
 
 #print CategoryTheory.CostructuredArrow.eq_mk /-
 /-- Eta rule for costructured arrows. Prefer `costructured_arrow.eta`, as equality of objects tends
@@ -388,19 +438,25 @@ def map (f : T ⟶ T') : CostructuredArrow S T ⥤ CostructuredArrow S T' :=
 #align category_theory.costructured_arrow.map CategoryTheory.CostructuredArrow.map
 -/
 
+#print CategoryTheory.CostructuredArrow.map_mk /-
 @[simp]
 theorem map_mk {f : S.obj Y ⟶ T} (g : T ⟶ T') : (map g).obj (mk f) = mk (f ≫ g) :=
   rfl
 #align category_theory.costructured_arrow.map_mk CategoryTheory.CostructuredArrow.map_mk
+-/
 
+#print CategoryTheory.CostructuredArrow.map_id /-
 @[simp]
 theorem map_id {f : CostructuredArrow S T} : (map (𝟙 T)).obj f = f := by rw [eq_mk f]; simp
 #align category_theory.costructured_arrow.map_id CategoryTheory.CostructuredArrow.map_id
+-/
 
+#print CategoryTheory.CostructuredArrow.map_comp /-
 @[simp]
 theorem map_comp {f : T ⟶ T'} {f' : T' ⟶ T''} {h : CostructuredArrow S T} :
     (map (f ≫ f')).obj h = (map f').obj ((map f).obj h) := by rw [eq_mk h]; simp
 #align category_theory.costructured_arrow.map_comp CategoryTheory.CostructuredArrow.map_comp
+-/
 
 #print CategoryTheory.CostructuredArrow.proj_reflectsIsomorphisms /-
 instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T)
@@ -413,6 +469,7 @@ open CategoryTheory.Limits
 
 attribute [local tidy] tactic.discrete_cases
 
+#print CategoryTheory.CostructuredArrow.mkIdTerminal /-
 /-- The identity costructured arrow is terminal. -/
 def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y)))
     where
@@ -423,6 +480,7 @@ def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y)))
     apply S.map_injective
     simpa only [hom_mk_left, S.image_preimage, ← w m] using (category.comp_id _).symm
 #align category_theory.costructured_arrow.mk_id_terminal CategoryTheory.CostructuredArrow.mkIdTerminal
+-/
 
 variable {A : Type u₃} [Category.{v₃} A] {B : Type u₄} [Category.{v₄} B]
 
@@ -434,6 +492,7 @@ def pre (F : B ⥤ C) (G : C ⥤ D) (S : D) : CostructuredArrow (F ⋙ G) S ⥤
 #align category_theory.costructured_arrow.pre CategoryTheory.CostructuredArrow.pre
 -/
 
+#print CategoryTheory.CostructuredArrow.post /-
 /-- The functor `(F, S) ⥤ (F ⋙ G, G(S))`. -/
 @[simps]
 def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :
@@ -442,7 +501,9 @@ def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :
   obj X := CostructuredArrow.mk (G.map X.Hom)
   map X Y f := CostructuredArrow.homMk f.left (by simp [functor.comp_map, ← G.map_comp, ← f.w])
 #align category_theory.costructured_arrow.post CategoryTheory.CostructuredArrow.post
+-/
 
+#print CategoryTheory.CostructuredArrow.small_proj_preimage_of_locallySmall /-
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) :=
   by
@@ -450,6 +511,7 @@ instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢]
     infer_instance
   exact Set.ext fun X => ⟨fun h => ⟨⟨⟨_, h⟩, X.Hom⟩, (eq_mk _).symm⟩, by tidy⟩
 #align category_theory.costructured_arrow.small_proj_preimage_of_locally_small CategoryTheory.CostructuredArrow.small_proj_preimage_of_locallySmall
+-/
 
 end CostructuredArrow
 
@@ -539,6 +601,7 @@ def toStructuredArrow' (F : C ⥤ D) (d : D) : (CostructuredArrow F.op (op d))
 
 end CostructuredArrow
 
+#print CategoryTheory.structuredArrowOpEquivalence /-
 /-- For a functor `F : C ⥤ D` and an object `d : D`, the category of structured arrows `d ⟶ F.obj c`
 is contravariantly equivalent to the category of costructured arrows `F.op.obj c ⟶ op d`.
 -/
@@ -556,7 +619,9 @@ def structuredArrowOpEquivalence (F : C ⥤ D) (d : D) :
         @CostructuredArrow.isoMk _ _ _ _ _ _ (CostructuredArrow.mk X.Hom) X (Iso.refl _) (by tidy))
       fun X Y f => by ext; dsimp; simp)
 #align category_theory.structured_arrow_op_equivalence CategoryTheory.structuredArrowOpEquivalence
+-/
 
+#print CategoryTheory.costructuredArrowOpEquivalence /-
 /-- For a functor `F : C ⥤ D` and an object `d : D`, the category of costructured arrows
 `F.obj c ⟶ d` is contravariantly equivalent to the category of structured arrows
 `op d ⟶ F.op.obj c`.
@@ -575,6 +640,7 @@ def costructuredArrowOpEquivalence (F : C ⥤ D) (d : D) :
         @StructuredArrow.isoMk _ _ _ _ _ _ (StructuredArrow.mk X.Hom) X (Iso.refl _) (by tidy))
       fun X Y f => by ext; dsimp; simp)
 #align category_theory.costructured_arrow_op_equivalence CategoryTheory.costructuredArrowOpEquivalence
+-/
 
 end CategoryTheory

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -42,7 +42,8 @@ and morphisms `C`-morphisms `Y ⟶ Y'` making the obvious triangle commute.
 -/
 @[nolint has_nonempty_instance]
 def StructuredArrow (S : D) (T : C ⥤ D) :=
-  Comma (Functor.fromPUnit S) T deriving Category
+  Comma (Functor.fromPUnit S) T
+deriving Category
 #align category_theory.structured_arrow CategoryTheory.StructuredArrow
 -/
 
@@ -157,7 +158,7 @@ instance epi_homMk {A B : StructuredArrow S T} (f : A.right ⟶ B.right) (w) [h
 #print CategoryTheory.StructuredArrow.eq_mk /-
 /-- Eta rule for structured arrows. Prefer `structured_arrow.eta`, since equality of objects tends
     to cause problems. -/
-theorem eq_mk (f : StructuredArrow S T) : f = mk f.Hom := by cases f; congr ; ext
+theorem eq_mk (f : StructuredArrow S T) : f = mk f.Hom := by cases f; congr; ext
 #align category_theory.structured_arrow.eq_mk CategoryTheory.StructuredArrow.eq_mk
 -/
 
@@ -240,7 +241,7 @@ def post (S : C) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S F ⥤ Structure
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) :=
   by
-  suffices (proj S T).obj ⁻¹' 𝒢 = Set.range fun f : ΣG : 𝒢, S ⟶ T.obj G => mk f.2 by rw [this];
+  suffices (proj S T).obj ⁻¹' 𝒢 = Set.range fun f : Σ G : 𝒢, S ⟶ T.obj G => mk f.2 by rw [this];
     infer_instance
   exact Set.ext fun X => ⟨fun h => ⟨⟨⟨_, h⟩, X.Hom⟩, (eq_mk _).symm⟩, by tidy⟩
 #align category_theory.structured_arrow.small_proj_preimage_of_locally_small CategoryTheory.StructuredArrow.small_proj_preimage_of_locallySmall
@@ -254,7 +255,8 @@ and morphisms `C`-morphisms `Y ⟶ Y'` making the obvious triangle commute.
 -/
 @[nolint has_nonempty_instance]
 def CostructuredArrow (S : C ⥤ D) (T : D) :=
-  Comma S (Functor.fromPUnit T)deriving Category
+  Comma S (Functor.fromPUnit T)
+deriving Category
 #align category_theory.costructured_arrow CategoryTheory.CostructuredArrow
 -/
 
@@ -359,7 +361,7 @@ instance epi_homMk {A B : CostructuredArrow S T} (f : A.left ⟶ B.left) (w) [h
 #print CategoryTheory.CostructuredArrow.eq_mk /-
 /-- Eta rule for costructured arrows. Prefer `costructured_arrow.eta`, as equality of objects tends
     to cause problems. -/
-theorem eq_mk (f : CostructuredArrow S T) : f = mk f.Hom := by cases f; congr ; ext
+theorem eq_mk (f : CostructuredArrow S T) : f = mk f.Hom := by cases f; congr; ext
 #align category_theory.costructured_arrow.eq_mk CategoryTheory.CostructuredArrow.eq_mk
 -/
 
@@ -444,7 +446,7 @@ def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) :=
   by
-  suffices (proj S T).obj ⁻¹' 𝒢 = Set.range fun f : ΣG : 𝒢, S.obj G ⟶ T => mk f.2 by rw [this];
+  suffices (proj S T).obj ⁻¹' 𝒢 = Set.range fun f : Σ G : 𝒢, S.obj G ⟶ T => mk f.2 by rw [this];
     infer_instance
   exact Set.ext fun X => ⟨fun h => ⟨⟨⟨_, h⟩, X.Hom⟩, (eq_mk _).symm⟩, by tidy⟩
 #align category_theory.costructured_arrow.small_proj_preimage_of_locally_small CategoryTheory.CostructuredArrow.small_proj_preimage_of_locallySmall

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -58,61 +58,31 @@ def proj (S : D) (T : C ⥤ D) : StructuredArrow S T ⥤ C :=
 
 variable {S S' S'' : D} {Y Y' : C} {T : C ⥤ D}
 
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 /-- Construct a structured arrow from a morphism. -/
 def mk (f : S ⟶ T.obj Y) : StructuredArrow S T :=
   ⟨⟨⟨⟩⟩, Y, f⟩
 #align category_theory.structured_arrow.mk CategoryTheory.StructuredArrow.mk
 
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 @[simp]
 theorem mk_left (f : S ⟶ T.obj Y) : (mk f).left = ⟨⟨⟩⟩ :=
   rfl
 #align category_theory.structured_arrow.mk_left CategoryTheory.StructuredArrow.mk_left
 
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 @[simp]
 theorem mk_right (f : S ⟶ T.obj Y) : (mk f).right = Y :=
   rfl
 #align category_theory.structured_arrow.mk_right CategoryTheory.StructuredArrow.mk_right
 
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 @[simp]
 theorem mk_hom_eq_self (f : S ⟶ T.obj Y) : (mk f).Hom = f :=
   rfl
 #align category_theory.structured_arrow.mk_hom_eq_self CategoryTheory.StructuredArrow.mk_hom_eq_self
 
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 @[simp, reassoc]
 theorem w {A B : StructuredArrow S T} (f : A ⟶ B) : A.Hom ≫ T.map f.right = B.Hom := by
   have := f.w <;> tidy
 #align category_theory.structured_arrow.w CategoryTheory.StructuredArrow.w
 
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 /-- To construct a morphism of structured arrows,
 we need a morphism of the objects underlying the target,
 and to check that the triangle commutes.
@@ -125,12 +95,6 @@ def homMk {f f' : StructuredArrow S T} (g : f.right ⟶ f'.right) (w : f.Hom ≫
   w' := by dsimp; simpa using w.symm
 #align category_theory.structured_arrow.hom_mk CategoryTheory.StructuredArrow.homMk
 
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 /-- Given a structured arrow `X ⟶ F(U)`, and an arrow `U ⟶ Y`, we can construct a morphism of
 structured arrow given by `(X ⟶ F(U)) ⟶ (X ⟶ F(U) ⟶ F(Y))`.
 -/
@@ -140,9 +104,6 @@ def homMk' {F : C ⥤ D} {X : D} {Y : C} (U : StructuredArrow X F) (f : U.right
   right := f
 #align category_theory.structured_arrow.hom_mk' CategoryTheory.StructuredArrow.homMk'
 
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 /-- To construct an isomorphism of structured arrows,
 we need an isomorphism of the objects underlying the target,
 and to check that the triangle commutes.
@@ -183,17 +144,11 @@ theorem epi_of_epi_right {A B : StructuredArrow S T} (f : A ⟶ B) [h : Epi f.ri
 #align category_theory.structured_arrow.epi_of_epi_right CategoryTheory.StructuredArrow.epi_of_epi_right
 -/
 
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 instance mono_homMk {A B : StructuredArrow S T} (f : A.right ⟶ B.right) (w) [h : Mono f] :
     Mono (homMk f w) :=
   (proj S T).mono_of_mono_map h
 #align category_theory.structured_arrow.mono_hom_mk CategoryTheory.StructuredArrow.mono_homMk
 
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 instance epi_homMk {A B : StructuredArrow S T} (f : A.right ⟶ B.right) (w) [h : Epi f] :
     Epi (homMk f w) :=
   (proj S T).epi_of_epi_map h
@@ -229,33 +184,15 @@ def map (f : S ⟶ S') : StructuredArrow S' T ⥤ StructuredArrow S T :=
 #align category_theory.structured_arrow.map CategoryTheory.StructuredArrow.map
 -/
 
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 @[simp]
 theorem map_mk {f : S' ⟶ T.obj Y} (g : S ⟶ S') : (map g).obj (mk f) = mk (g ≫ f) :=
   rfl
 #align category_theory.structured_arrow.map_mk CategoryTheory.StructuredArrow.map_mk
 
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 @[simp]
 theorem map_id {f : StructuredArrow S T} : (map (𝟙 S)).obj f = f := by rw [eq_mk f]; simp
 #align category_theory.structured_arrow.map_id CategoryTheory.StructuredArrow.map_id
 
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 @[simp]
 theorem map_comp {f : S ⟶ S'} {f' : S' ⟶ S''} {h : StructuredArrow S'' T} :
     (map (f ≫ f')).obj h = (map f).obj ((map f').obj h) := by rw [eq_mk h]; simp
@@ -272,12 +209,6 @@ open CategoryTheory.Limits
 
 attribute [local tidy] tactic.discrete_cases
 
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 /-- The identity structured arrow is initial. -/
 def mkIdInitial [Full T] [Faithful T] : IsInitial (mk (𝟙 (T.obj Y)))
     where
@@ -298,12 +229,6 @@ def pre (S : D) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S (F ⋙ G) ⥤ St
 #align category_theory.structured_arrow.pre CategoryTheory.StructuredArrow.pre
 -/
 
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 /-- The functor `(S, F) ⥤ (G(S), F ⋙ G)`. -/
 @[simps]
 def post (S : C) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S F ⥤ StructuredArrow (G.obj S) (F ⋙ G)
@@ -312,12 +237,6 @@ def post (S : C) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S F ⥤ Structure
   map X Y f := StructuredArrow.homMk f.right (by simp [functor.comp_map, ← G.map_comp, ← f.w])
 #align category_theory.structured_arrow.post CategoryTheory.StructuredArrow.post
 
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 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) :=
   by
@@ -351,60 +270,30 @@ def proj (S : C ⥤ D) (T : D) : CostructuredArrow S T ⥤ C :=
 
 variable {T T' T'' : D} {Y Y' : C} {S : C ⥤ D}
 
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 /-- Construct a costructured arrow from a morphism. -/
 def mk (f : S.obj Y ⟶ T) : CostructuredArrow S T :=
   ⟨Y, ⟨⟨⟩⟩, f⟩
 #align category_theory.costructured_arrow.mk CategoryTheory.CostructuredArrow.mk
 
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 @[simp]
 theorem mk_left (f : S.obj Y ⟶ T) : (mk f).left = Y :=
   rfl
 #align category_theory.costructured_arrow.mk_left CategoryTheory.CostructuredArrow.mk_left
 
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 @[simp]
 theorem mk_right (f : S.obj Y ⟶ T) : (mk f).right = ⟨⟨⟩⟩ :=
   rfl
 #align category_theory.costructured_arrow.mk_right CategoryTheory.CostructuredArrow.mk_right
 
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 @[simp]
 theorem mk_hom_eq_self (f : S.obj Y ⟶ T) : (mk f).Hom = f :=
   rfl
 #align category_theory.costructured_arrow.mk_hom_eq_self CategoryTheory.CostructuredArrow.mk_hom_eq_self
 
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 @[simp, reassoc]
 theorem w {A B : CostructuredArrow S T} (f : A ⟶ B) : S.map f.left ≫ B.Hom = A.Hom := by tidy
 #align category_theory.costructured_arrow.w CategoryTheory.CostructuredArrow.w
 
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 /-- To construct a morphism of costructured arrows,
 we need a morphism of the objects underlying the source,
 and to check that the triangle commutes.
@@ -417,9 +306,6 @@ def homMk {f f' : CostructuredArrow S T} (g : f.left ⟶ f'.left) (w : S.map g 
   w' := by simpa [eq_to_hom_map] using w
 #align category_theory.costructured_arrow.hom_mk CategoryTheory.CostructuredArrow.homMk
 
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 /-- To construct an isomorphism of costructured arrows,
 we need an isomorphism of the objects underlying the source,
 and to check that the triangle commutes.
@@ -460,17 +346,11 @@ theorem epi_of_epi_left {A B : CostructuredArrow S T} (f : A ⟶ B) [h : Epi f.l
 #align category_theory.costructured_arrow.epi_of_epi_left CategoryTheory.CostructuredArrow.epi_of_epi_left
 -/
 
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 instance mono_homMk {A B : CostructuredArrow S T} (f : A.left ⟶ B.left) (w) [h : Mono f] :
     Mono (homMk f w) :=
   (proj S T).mono_of_mono_map h
 #align category_theory.costructured_arrow.mono_hom_mk CategoryTheory.CostructuredArrow.mono_homMk
 
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 instance epi_homMk {A B : CostructuredArrow S T} (f : A.left ⟶ B.left) (w) [h : Epi f] :
     Epi (homMk f w) :=
   (proj S T).epi_of_epi_map h
@@ -506,33 +386,15 @@ def map (f : T ⟶ T') : CostructuredArrow S T ⥤ CostructuredArrow S T' :=
 #align category_theory.costructured_arrow.map CategoryTheory.CostructuredArrow.map
 -/
 
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 @[simp]
 theorem map_mk {f : S.obj Y ⟶ T} (g : T ⟶ T') : (map g).obj (mk f) = mk (f ≫ g) :=
   rfl
 #align category_theory.costructured_arrow.map_mk CategoryTheory.CostructuredArrow.map_mk
 
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 @[simp]
 theorem map_id {f : CostructuredArrow S T} : (map (𝟙 T)).obj f = f := by rw [eq_mk f]; simp
 #align category_theory.costructured_arrow.map_id CategoryTheory.CostructuredArrow.map_id
 
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 @[simp]
 theorem map_comp {f : T ⟶ T'} {f' : T' ⟶ T''} {h : CostructuredArrow S T} :
     (map (f ≫ f')).obj h = (map f').obj ((map f).obj h) := by rw [eq_mk h]; simp
@@ -549,12 +411,6 @@ open CategoryTheory.Limits
 
 attribute [local tidy] tactic.discrete_cases
 
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 /-- The identity costructured arrow is terminal. -/
 def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y)))
     where
@@ -576,12 +432,6 @@ def pre (F : B ⥤ C) (G : C ⥤ D) (S : D) : CostructuredArrow (F ⋙ G) S ⥤
 #align category_theory.costructured_arrow.pre CategoryTheory.CostructuredArrow.pre
 -/
 
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 /-- The functor `(F, S) ⥤ (F ⋙ G, G(S))`. -/
 @[simps]
 def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :
@@ -591,12 +441,6 @@ def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :
   map X Y f := CostructuredArrow.homMk f.left (by simp [functor.comp_map, ← G.map_comp, ← f.w])
 #align category_theory.costructured_arrow.post CategoryTheory.CostructuredArrow.post
 
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 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) :=
   by
@@ -693,12 +537,6 @@ def toStructuredArrow' (F : C ⥤ D) (d : D) : (CostructuredArrow F.op (op d))
 
 end CostructuredArrow
 
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 /-- For a functor `F : C ⥤ D` and an object `d : D`, the category of structured arrows `d ⟶ F.obj c`
 is contravariantly equivalent to the category of costructured arrows `F.op.obj c ⟶ op d`.
 -/
@@ -717,12 +555,6 @@ def structuredArrowOpEquivalence (F : C ⥤ D) (d : D) :
       fun X Y f => by ext; dsimp; simp)
 #align category_theory.structured_arrow_op_equivalence CategoryTheory.structuredArrowOpEquivalence
 
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 /-- For a functor `F : C ⥤ D` and an object `d : D`, the category of costructured arrows
 `F.obj c ⟶ d` is contravariantly equivalent to the category of structured arrows
 `op d ⟶ F.op.obj c`.

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -122,9 +122,7 @@ def homMk {f f' : StructuredArrow S T} (g : f.right ⟶ f'.right) (w : f.Hom ≫
     f ⟶ f' where
   left := eqToHom (by ext)
   right := g
-  w' := by
-    dsimp
-    simpa using w.symm
+  w' := by dsimp; simpa using w.symm
 #align category_theory.structured_arrow.hom_mk CategoryTheory.StructuredArrow.homMk
 
 /- warning: category_theory.structured_arrow.hom_mk' -> CategoryTheory.StructuredArrow.homMk' is a dubious translation:
@@ -204,11 +202,7 @@ instance epi_homMk {A B : StructuredArrow S T} (f : A.right ⟶ B.right) (w) [h
 #print CategoryTheory.StructuredArrow.eq_mk /-
 /-- Eta rule for structured arrows. Prefer `structured_arrow.eta`, since equality of objects tends
     to cause problems. -/
-theorem eq_mk (f : StructuredArrow S T) : f = mk f.Hom :=
-  by
-  cases f
-  congr
-  ext
+theorem eq_mk (f : StructuredArrow S T) : f = mk f.Hom := by cases f; congr ; ext
 #align category_theory.structured_arrow.eq_mk CategoryTheory.StructuredArrow.eq_mk
 -/
 
@@ -253,10 +247,7 @@ but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] {S : D} {T : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2} {f : CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T}, Eq.{max (succ u3) (succ u2)} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (Prefunctor.obj.{max (succ u2) (succ u1), max (succ u2) (succ u1), max u2 u3, max u2 u3} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 u3} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 u3} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.instCategoryStructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T))) (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 u3} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 u3} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.instCategoryStructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T))) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, max u2 u3, max u2 u3} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.instCategoryStructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.instCategoryStructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.StructuredArrow.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 S S T (CategoryTheory.CategoryStruct.id.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2) S))) f) f
 Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.map_id CategoryTheory.StructuredArrow.map_idₓ'. -/
 @[simp]
-theorem map_id {f : StructuredArrow S T} : (map (𝟙 S)).obj f = f :=
-  by
-  rw [eq_mk f]
-  simp
+theorem map_id {f : StructuredArrow S T} : (map (𝟙 S)).obj f = f := by rw [eq_mk f]; simp
 #align category_theory.structured_arrow.map_id CategoryTheory.StructuredArrow.map_id
 
 /- warning: category_theory.structured_arrow.map_comp -> CategoryTheory.StructuredArrow.map_comp is a dubious translation:
@@ -267,10 +258,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.map_comp CategoryTheory.StructuredArrow.map_compₓ'. -/
 @[simp]
 theorem map_comp {f : S ⟶ S'} {f' : S' ⟶ S''} {h : StructuredArrow S'' T} :
-    (map (f ≫ f')).obj h = (map f).obj ((map f').obj h) :=
-  by
-  rw [eq_mk h]
-  simp
+    (map (f ≫ f')).obj h = (map f).obj ((map f').obj h) := by rw [eq_mk h]; simp
 #align category_theory.structured_arrow.map_comp CategoryTheory.StructuredArrow.map_comp
 
 #print CategoryTheory.StructuredArrow.proj_reflectsIsomorphisms /-
@@ -293,11 +281,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.struct
 /-- The identity structured arrow is initial. -/
 def mkIdInitial [Full T] [Faithful T] : IsInitial (mk (𝟙 (T.obj Y)))
     where
-  desc c :=
-    homMk (T.preimage c.pt.Hom)
-      (by
-        dsimp
-        simp)
+  desc c := homMk (T.preimage c.pt.Hom) (by dsimp; simp)
   uniq c m _ := by
     ext
     apply T.map_injective
@@ -337,9 +321,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.struct
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) :=
   by
-  suffices (proj S T).obj ⁻¹' 𝒢 = Set.range fun f : ΣG : 𝒢, S ⟶ T.obj G => mk f.2
-    by
-    rw [this]
+  suffices (proj S T).obj ⁻¹' 𝒢 = Set.range fun f : ΣG : 𝒢, S ⟶ T.obj G => mk f.2 by rw [this];
     infer_instance
   exact Set.ext fun X => ⟨fun h => ⟨⟨⟨_, h⟩, X.Hom⟩, (eq_mk _).symm⟩, by tidy⟩
 #align category_theory.structured_arrow.small_proj_preimage_of_locally_small CategoryTheory.StructuredArrow.small_proj_preimage_of_locallySmall
@@ -497,11 +479,7 @@ instance epi_homMk {A B : CostructuredArrow S T} (f : A.left ⟶ B.left) (w) [h
 #print CategoryTheory.CostructuredArrow.eq_mk /-
 /-- Eta rule for costructured arrows. Prefer `costructured_arrow.eta`, as equality of objects tends
     to cause problems. -/
-theorem eq_mk (f : CostructuredArrow S T) : f = mk f.Hom :=
-  by
-  cases f
-  congr
-  ext
+theorem eq_mk (f : CostructuredArrow S T) : f = mk f.Hom := by cases f; congr ; ext
 #align category_theory.costructured_arrow.eq_mk CategoryTheory.CostructuredArrow.eq_mk
 -/
 
@@ -546,10 +524,7 @@ but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.map_id CategoryTheory.CostructuredArrow.map_idₓ'. -/
 @[simp]
-theorem map_id {f : CostructuredArrow S T} : (map (𝟙 T)).obj f = f :=
-  by
-  rw [eq_mk f]
-  simp
+theorem map_id {f : CostructuredArrow S T} : (map (𝟙 T)).obj f = f := by rw [eq_mk f]; simp
 #align category_theory.costructured_arrow.map_id CategoryTheory.CostructuredArrow.map_id
 
 /- warning: category_theory.costructured_arrow.map_comp -> CategoryTheory.CostructuredArrow.map_comp is a dubious translation:
@@ -560,10 +535,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.map_comp CategoryTheory.CostructuredArrow.map_compₓ'. -/
 @[simp]
 theorem map_comp {f : T ⟶ T'} {f' : T' ⟶ T''} {h : CostructuredArrow S T} :
-    (map (f ≫ f')).obj h = (map f').obj ((map f).obj h) :=
-  by
-  rw [eq_mk h]
-  simp
+    (map (f ≫ f')).obj h = (map f').obj ((map f).obj h) := by rw [eq_mk h]; simp
 #align category_theory.costructured_arrow.map_comp CategoryTheory.CostructuredArrow.map_comp
 
 #print CategoryTheory.CostructuredArrow.proj_reflectsIsomorphisms /-
@@ -586,11 +558,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.costru
 /-- The identity costructured arrow is terminal. -/
 def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y)))
     where
-  lift c :=
-    homMk (S.preimage c.pt.Hom)
-      (by
-        dsimp
-        simp)
+  lift c := homMk (S.preimage c.pt.Hom) (by dsimp; simp)
   uniq := by
     rintro c m -
     ext
@@ -632,9 +600,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.costru
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) :=
   by
-  suffices (proj S T).obj ⁻¹' 𝒢 = Set.range fun f : ΣG : 𝒢, S.obj G ⟶ T => mk f.2
-    by
-    rw [this]
+  suffices (proj S T).obj ⁻¹' 𝒢 = Set.range fun f : ΣG : 𝒢, S.obj G ⟶ T => mk f.2 by rw [this];
     infer_instance
   exact Set.ext fun X => ⟨fun h => ⟨⟨⟨_, h⟩, X.Hom⟩, (eq_mk _).symm⟩, by tidy⟩
 #align category_theory.costructured_arrow.small_proj_preimage_of_locally_small CategoryTheory.CostructuredArrow.small_proj_preimage_of_locallySmall

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -103,10 +103,7 @@ theorem mk_hom_eq_self (f : S ⟶ T.obj Y) : (mk f).Hom = f :=
 #align category_theory.structured_arrow.mk_hom_eq_self CategoryTheory.StructuredArrow.mk_hom_eq_self
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.w CategoryTheory.StructuredArrow.wₓ'. -/
 @[simp, reassoc]
 theorem w {A B : StructuredArrow S T} (f : A ⟶ B) : A.Hom ≫ T.map f.right = B.Hom := by
@@ -114,10 +111,7 @@ theorem w {A B : StructuredArrow S T} (f : A ⟶ B) : A.Hom ≫ T.map f.right =
 #align category_theory.structured_arrow.w CategoryTheory.StructuredArrow.w
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.hom_mk CategoryTheory.StructuredArrow.homMkₓ'. -/
 /-- To construct a morphism of structured arrows,
 we need a morphism of the objects underlying the target,
@@ -149,10 +143,7 @@ def homMk' {F : C ⥤ D} {X : D} {Y : C} (U : StructuredArrow X F) (f : U.right
 #align category_theory.structured_arrow.hom_mk' CategoryTheory.StructuredArrow.homMk'
 
 /- warning: category_theory.structured_arrow.iso_mk -> CategoryTheory.StructuredArrow.isoMk is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.iso_mk CategoryTheory.StructuredArrow.isoMkₓ'. -/
 /-- To construct an isomorphism of structured arrows,
 we need an isomorphism of the objects underlying the target,
@@ -195,10 +186,7 @@ theorem epi_of_epi_right {A B : StructuredArrow S T} (f : A ⟶ B) [h : Epi f.ri
 -/
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.mono_hom_mk CategoryTheory.StructuredArrow.mono_homMkₓ'. -/
 instance mono_homMk {A B : StructuredArrow S T} (f : A.right ⟶ B.right) (w) [h : Mono f] :
     Mono (homMk f w) :=
@@ -206,10 +194,7 @@ instance mono_homMk {A B : StructuredArrow S T} (f : A.right ⟶ B.right) (w) [h
 #align category_theory.structured_arrow.mono_hom_mk CategoryTheory.StructuredArrow.mono_homMk
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.epi_hom_mk CategoryTheory.StructuredArrow.epi_homMkₓ'. -/
 instance epi_homMk {A B : StructuredArrow S T} (f : A.right ⟶ B.right) (w) [h : Epi f] :
     Epi (homMk f w) :=
@@ -429,20 +414,14 @@ theorem mk_hom_eq_self (f : S.obj Y ⟶ T) : (mk f).Hom = f :=
 #align category_theory.costructured_arrow.mk_hom_eq_self CategoryTheory.CostructuredArrow.mk_hom_eq_self
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.w CategoryTheory.CostructuredArrow.wₓ'. -/
 @[simp, reassoc]
 theorem w {A B : CostructuredArrow S T} (f : A ⟶ B) : S.map f.left ≫ B.Hom = A.Hom := by tidy
 #align category_theory.costructured_arrow.w CategoryTheory.CostructuredArrow.w
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.hom_mk CategoryTheory.CostructuredArrow.homMkₓ'. -/
 /-- To construct a morphism of costructured arrows,
 we need a morphism of the objects underlying the source,
@@ -457,10 +436,7 @@ def homMk {f f' : CostructuredArrow S T} (g : f.left ⟶ f'.left) (w : S.map g 
 #align category_theory.costructured_arrow.hom_mk CategoryTheory.CostructuredArrow.homMk
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.iso_mk CategoryTheory.CostructuredArrow.isoMkₓ'. -/
 /-- To construct an isomorphism of costructured arrows,
 we need an isomorphism of the objects underlying the source,
@@ -503,10 +479,7 @@ theorem epi_of_epi_left {A B : CostructuredArrow S T} (f : A ⟶ B) [h : Epi f.l
 -/
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.mono_hom_mk CategoryTheory.CostructuredArrow.mono_homMkₓ'. -/
 instance mono_homMk {A B : CostructuredArrow S T} (f : A.left ⟶ B.left) (w) [h : Mono f] :
     Mono (homMk f w) :=
@@ -514,10 +487,7 @@ instance mono_homMk {A B : CostructuredArrow S T} (f : A.left ⟶ B.left) (w) [h
 #align category_theory.costructured_arrow.mono_hom_mk CategoryTheory.CostructuredArrow.mono_homMk
 
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u2, u3, u2, u4} C _inst_1 (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 S (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T) A)) [h : CategoryTheory.Epi.{u1, u3} C _inst_1 (CategoryTheory.Comma.left.{u1, u2, u2, u3, u2, u4} C _inst_1 (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 S (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T) A) (CategoryTheory.Comma.left.{u1, u2, u2, u3, u2, u4} C _inst_1 (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 S (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T) B) f], CategoryTheory.Epi.{max u2 u1, max u3 u2} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.instCategoryCostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) A B (CategoryTheory.CostructuredArrow.homMk.{u1, u2, u3, u4} C _inst_1 D _inst_2 T S A B f w)
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.epi_hom_mk CategoryTheory.CostructuredArrow.epi_homMkₓ'. -/
 instance epi_homMk {A B : CostructuredArrow S T} (f : A.left ⟶ B.left) (w) [h : Epi f] :
     Epi (homMk f w) :=

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -108,7 +108,7 @@ lean 3 declaration is
 but is expected to have type
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(CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) C _inst_1 D _inst_2 (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 S) T A)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 T) (CategoryTheory.Comma.right.{u2, u1, u2, u2, u3, u4} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) C _inst_1 D _inst_2 (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 S) T B)) (CategoryTheory.Comma.hom.{u2, u1, u2, u2, u3, u4} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) C _inst_1 D _inst_2 (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 S) T A) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 T) (CategoryTheory.Comma.right.{u2, u1, u2, u2, u3, u4} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) C _inst_1 D _inst_2 (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 S) T A) (CategoryTheory.Comma.right.{u2, u1, u2, u2, u3, u4} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) C _inst_1 D _inst_2 (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 S) T B) (CategoryTheory.CommaMorphism.right.{u2, u1, u2, u2, u3, u4} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) C _inst_1 D _inst_2 (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 S) T A B f))) (CategoryTheory.Comma.hom.{u2, u1, u2, u2, u3, u4} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) C _inst_1 D _inst_2 (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 S) T B)
 Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.w CategoryTheory.StructuredArrow.wₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem w {A B : StructuredArrow S T} (f : A ⟶ B) : A.Hom ≫ T.map f.right = B.Hom := by
   have := f.w <;> tidy
 #align category_theory.structured_arrow.w CategoryTheory.StructuredArrow.w
@@ -434,7 +434,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] {T : D} {S : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2} {A : CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T} {B : CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T} (f : Quiver.Hom.{max (succ u1) (succ u2), max u3 u2} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max u3 u2} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max u3 u2} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.instCategoryCostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T))) A B), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 S) (CategoryTheory.Comma.left.{u1, u2, u2, u3, u2, u4} C _inst_1 (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 S (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T) A)) (Prefunctor.obj.{succ u2, succ u2, u2, u4} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.CategoryStruct.toQuiver.{u2, u2} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.Category.toCategoryStruct.{u2, u2} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}))) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u2, u4} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T)) (CategoryTheory.Comma.right.{u1, u2, u2, u3, u2, u4} C _inst_1 (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 S (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T) B))) (CategoryTheory.CategoryStruct.comp.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 S) (CategoryTheory.Comma.left.{u1, u2, u2, u3, u2, u4} C _inst_1 (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 S (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T) A)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 S) (CategoryTheory.Comma.left.{u1, u2, u2, u3, u2, u4} C _inst_1 (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 S (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T) B)) (Prefunctor.obj.{succ u2, succ u2, u2, u4} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.CategoryStruct.toQuiver.{u2, u2} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.Category.toCategoryStruct.{u2, u2} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}))) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u2, u4} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T)) (CategoryTheory.Comma.right.{u1, u2, u2, u3, u2, u4} C _inst_1 (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 S (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T) B)) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 S) (CategoryTheory.Comma.left.{u1, u2, u2, u3, u2, u4} C _inst_1 (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 S (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T) A) (CategoryTheory.Comma.left.{u1, u2, u2, u3, u2, u4} C _inst_1 (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 S (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T) B) (CategoryTheory.CommaMorphism.left.{u1, u2, u2, u3, u2, u4} C _inst_1 (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 S (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T) A B f)) (CategoryTheory.Comma.hom.{u1, u2, u2, u3, u2, u4} C _inst_1 (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 S (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T) B)) (CategoryTheory.Comma.hom.{u1, u2, u2, u3, u2, u4} C _inst_1 (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) D _inst_2 S (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 T) A)
 Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.w CategoryTheory.CostructuredArrow.wₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem w {A B : CostructuredArrow S T} (f : A ⟶ B) : S.map f.left ≫ B.Hom = A.Hom := by tidy
 #align category_theory.costructured_arrow.w CategoryTheory.CostructuredArrow.w

bump to nightly-2023-04-18-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/49b7f94aab3a3bdca1f9f34c5d818afb253b3993

c37d1701

Diff

@@ -761,7 +761,7 @@ end CostructuredArrow
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (d : D), CategoryTheory.Equivalence.{max u2 u1, max u1 u2, max u3 u2, max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 d F)) (CategoryTheory.Category.opposite.{max u2 u1, max u3 u2} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 d F) (CategoryTheory.StructuredArrow.category.{u2, u4, u3, u1} C _inst_1 D _inst_2 d F)) (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) (Opposite.{succ u4} D) (CategoryTheory.Category.opposite.{u2, u4} D _inst_2) (CategoryTheory.Functor.op.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) (Opposite.op.{succ u4} D d)) (CategoryTheory.CostructuredArrow.category.{u2, u4, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) (Opposite.{succ u4} D) (CategoryTheory.Category.opposite.{u2, u4} D _inst_2) (CategoryTheory.Functor.op.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) (Opposite.op.{succ u4} D d))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (d : D), CategoryTheory.Equivalence.{max u1 u2, max u1 u2, max u3 u2, max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 d F)) (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) (Opposite.{succ u4} D) (CategoryTheory.Category.opposite.{u2, u4} D _inst_2) (CategoryTheory.Functor.op.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) (Opposite.op.{succ u4} D d)) (CategoryTheory.Category.opposite.{max u1 u2, max u3 u2} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 d F) (CategoryTheory.instCategoryStructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 d F)) (CategoryTheory.instCategoryCostructuredArrow.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) (Opposite.{succ u4} D) (CategoryTheory.Category.opposite.{u2, u4} D _inst_2) (CategoryTheory.Functor.op.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) (Opposite.op.{succ u4} D d))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (d : D), CategoryTheory.Equivalence.{max u1 u2, max u1 u2, max u3 u2, max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 d F)) (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) (Opposite.{succ u4} D) (CategoryTheory.Category.opposite.{u2, u4} D _inst_2) (CategoryTheory.Functor.op.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) (Opposite.op.{succ u4} D d)) (CategoryTheory.Category.opposite.{max u1 u2, max u3 u2} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 d F) (CategoryTheory.instCategoryStructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 d F)) (CategoryTheory.instCategoryCostructuredArrow.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) (Opposite.{succ u4} D) (CategoryTheory.Category.opposite.{u2, u4} D _inst_2) (CategoryTheory.Functor.op.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) (Opposite.op.{succ u4} D d))
 Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow_op_equivalence CategoryTheory.structuredArrowOpEquivalenceₓ'. -/
 /-- For a functor `F : C ⥤ D` and an object `d : D`, the category of structured arrows `d ⟶ F.obj c`
 is contravariantly equivalent to the category of costructured arrows `F.op.obj c ⟶ op d`.
@@ -785,7 +785,7 @@ def structuredArrowOpEquivalence (F : C ⥤ D) (d : D) :
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (d : D), CategoryTheory.Equivalence.{max u1 u2, max u2 u1, max u3 u2, max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 F d)) (CategoryTheory.Category.opposite.{max u1 u2, max u3 u2} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 F d) (CategoryTheory.CostructuredArrow.category.{u2, u4, u3, u1} C _inst_1 D _inst_2 F d)) (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) (Opposite.{succ u4} D) (CategoryTheory.Category.opposite.{u2, u4} D _inst_2) (Opposite.op.{succ u4} D d) (CategoryTheory.Functor.op.{u1, u2, u3, u4} C _inst_1 D _inst_2 F)) (CategoryTheory.StructuredArrow.category.{u2, u4, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) (Opposite.{succ u4} D) (CategoryTheory.Category.opposite.{u2, u4} D _inst_2) (Opposite.op.{succ u4} D d) (CategoryTheory.Functor.op.{u1, u2, u3, u4} C _inst_1 D _inst_2 F))
 but is expected to have type
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+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (d : D), CategoryTheory.Equivalence.{max u1 u2, max u1 u2, max u3 u2, max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 F d)) (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) (Opposite.{succ u4} D) (CategoryTheory.Category.opposite.{u2, u4} D _inst_2) (Opposite.op.{succ u4} D d) (CategoryTheory.Functor.op.{u1, u2, u3, u4} C _inst_1 D _inst_2 F)) (CategoryTheory.Category.opposite.{max u1 u2, max u3 u2} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 F d) (CategoryTheory.instCategoryCostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 F d)) (CategoryTheory.instCategoryStructuredArrow.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) (Opposite.{succ u4} D) (CategoryTheory.Category.opposite.{u2, u4} D _inst_2) (Opposite.op.{succ u4} D d) (CategoryTheory.Functor.op.{u1, u2, u3, u4} C _inst_1 D _inst_2 F))
 Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow_op_equivalence CategoryTheory.costructuredArrowOpEquivalenceₓ'. -/
 /-- For a functor `F : C ⥤ D` and an object `d : D`, the category of costructured arrows
 `F.obj c ⟶ d` is contravariantly equivalent to the category of structured arrows

bump to nightly-2023-03-09-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

75cac28a

Diff

@@ -288,11 +288,11 @@ theorem map_comp {f : S ⟶ S'} {f' : S' ⟶ S''} {h : StructuredArrow S'' T} :
   simp
 #align category_theory.structured_arrow.map_comp CategoryTheory.StructuredArrow.map_comp
 
-#print CategoryTheory.StructuredArrow.proj_reflects_iso /-
-instance proj_reflects_iso : ReflectsIsomorphisms (proj S T)
+#print CategoryTheory.StructuredArrow.proj_reflectsIsomorphisms /-
+instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T)
     where reflects Y Z f t :=
     ⟨⟨structured_arrow.hom_mk (inv ((proj S T).map f)) (by simp), by tidy⟩⟩
-#align category_theory.structured_arrow.proj_reflects_iso CategoryTheory.StructuredArrow.proj_reflects_iso
+#align category_theory.structured_arrow.proj_reflects_iso CategoryTheory.StructuredArrow.proj_reflectsIsomorphisms
 -/
 
 open CategoryTheory.Limits
@@ -596,11 +596,11 @@ theorem map_comp {f : T ⟶ T'} {f' : T' ⟶ T''} {h : CostructuredArrow S T} :
   simp
 #align category_theory.costructured_arrow.map_comp CategoryTheory.CostructuredArrow.map_comp
 
-#print CategoryTheory.CostructuredArrow.proj_reflects_iso /-
-instance proj_reflects_iso : ReflectsIsomorphisms (proj S T)
+#print CategoryTheory.CostructuredArrow.proj_reflectsIsomorphisms /-
+instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T)
     where reflects Y Z f t :=
     ⟨⟨costructured_arrow.hom_mk (inv ((proj S T).map f)) (by simp), by tidy⟩⟩
-#align category_theory.costructured_arrow.proj_reflects_iso CategoryTheory.CostructuredArrow.proj_reflects_iso
+#align category_theory.costructured_arrow.proj_reflects_iso CategoryTheory.CostructuredArrow.proj_reflectsIsomorphisms
 -/
 
 open CategoryTheory.Limits

bump to nightly-2023-03-09-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

061741a1

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz, Scott Morrison
 
 ! This file was ported from Lean 3 source module category_theory.structured_arrow
-! leanprover-community/mathlib commit 8a318021995877a44630c898d0b2bc376fceef3b
+! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.CategoryTheory.EssentiallySmall
 /-!
 # The category of "structured arrows"
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 For `T : C ⥤ D`, a `T`-structured arrow with source `S : D`
 is just a morphism `S ⟶ T.obj Y`, for some `Y : C`.

bump to nightly-2023-03-03-03

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

f2ed0adb

Diff

@@ -32,6 +32,7 @@ universe v₁ v₂ v₃ v₄ u₁ u₂ u₃ u₄
 
 variable {C : Type u₁} [Category.{v₁} C] {D : Type u₂} [Category.{v₂} D]
 
+#print CategoryTheory.StructuredArrow /-
 /-- The category of `T`-structured arrows with domain `S : D` (here `T : C ⥤ D`),
 has as its objects `D`-morphisms of the form `S ⟶ T Y`, for some `Y : C`,
 and morphisms `C`-morphisms `Y ⟶ Y'` making the obvious triangle commute.
@@ -40,42 +41,81 @@ and morphisms `C`-morphisms `Y ⟶ Y'` making the obvious triangle commute.
 def StructuredArrow (S : D) (T : C ⥤ D) :=
   Comma (Functor.fromPUnit S) T deriving Category
 #align category_theory.structured_arrow CategoryTheory.StructuredArrow
+-/
 
 namespace StructuredArrow
 
+#print CategoryTheory.StructuredArrow.proj /-
 /-- The obvious projection functor from structured arrows. -/
 @[simps]
 def proj (S : D) (T : C ⥤ D) : StructuredArrow S T ⥤ C :=
   Comma.snd _ _
 #align category_theory.structured_arrow.proj CategoryTheory.StructuredArrow.proj
+-/
 
 variable {S S' S'' : D} {Y Y' : C} {T : C ⥤ D}
 
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 /-- Construct a structured arrow from a morphism. -/
 def mk (f : S ⟶ T.obj Y) : StructuredArrow S T :=
   ⟨⟨⟨⟩⟩, Y, f⟩
 #align category_theory.structured_arrow.mk CategoryTheory.StructuredArrow.mk
 
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 @[simp]
 theorem mk_left (f : S ⟶ T.obj Y) : (mk f).left = ⟨⟨⟩⟩ :=
   rfl
 #align category_theory.structured_arrow.mk_left CategoryTheory.StructuredArrow.mk_left
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.mk_right CategoryTheory.StructuredArrow.mk_rightₓ'. -/
 @[simp]
 theorem mk_right (f : S ⟶ T.obj Y) : (mk f).right = Y :=
   rfl
 #align category_theory.structured_arrow.mk_right CategoryTheory.StructuredArrow.mk_right
 
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 @[simp]
 theorem mk_hom_eq_self (f : S ⟶ T.obj Y) : (mk f).Hom = f :=
   rfl
 #align category_theory.structured_arrow.mk_hom_eq_self CategoryTheory.StructuredArrow.mk_hom_eq_self
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.w CategoryTheory.StructuredArrow.wₓ'. -/
 @[simp, reassoc.1]
 theorem w {A B : StructuredArrow S T} (f : A ⟶ B) : A.Hom ≫ T.map f.right = B.Hom := by
   have := f.w <;> tidy
 #align category_theory.structured_arrow.w CategoryTheory.StructuredArrow.w
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.hom_mk CategoryTheory.StructuredArrow.homMkₓ'. -/
 /-- To construct a morphism of structured arrows,
 we need a morphism of the objects underlying the target,
 and to check that the triangle commutes.
@@ -90,6 +130,12 @@ def homMk {f f' : StructuredArrow S T} (g : f.right ⟶ f'.right) (w : f.Hom ≫
     simpa using w.symm
 #align category_theory.structured_arrow.hom_mk CategoryTheory.StructuredArrow.homMk
 
+/- warning: category_theory.structured_arrow.hom_mk' -> CategoryTheory.StructuredArrow.homMk' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.hom_mk' CategoryTheory.StructuredArrow.homMk'ₓ'. -/
 /-- Given a structured arrow `X ⟶ F(U)`, and an arrow `U ⟶ Y`, we can construct a morphism of
 structured arrow given by `(X ⟶ F(U)) ⟶ (X ⟶ F(U) ⟶ F(Y))`.
 -/
@@ -99,6 +145,12 @@ def homMk' {F : C ⥤ D} {X : D} {Y : C} (U : StructuredArrow X F) (f : U.right
   right := f
 #align category_theory.structured_arrow.hom_mk' CategoryTheory.StructuredArrow.homMk'
 
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] {S : D} {T : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2} {f : CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T} {f' : CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T} (g : CategoryTheory.Iso.{u1, u3} C _inst_1 (CategoryTheory.Comma.right.{u2, u1, u2, u2, u3, u4} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) C _inst_1 D _inst_2 (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 S) T f) (CategoryTheory.Comma.right.{u2, u1, u2, u2, u3, u4} (CategoryTheory.Discrete.{u2} PUnit.{succ u2}) (CategoryTheory.discreteCategory.{u2} PUnit.{succ u2}) C _inst_1 D _inst_2 (CategoryTheory.Functor.fromPUnit.{u2, u4} D _inst_2 S) T f')), (Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D 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+Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.iso_mk CategoryTheory.StructuredArrow.isoMkₓ'. -/
 /-- To construct an isomorphism of structured arrows,
 we need an isomorphism of the objects underlying the target,
 and to check that the triangle commutes.
@@ -109,36 +161,59 @@ def isoMk {f f' : StructuredArrow S T} (g : f.right ≅ f'.right) (w : f.Hom ≫
   Comma.isoMk (eqToIso (by ext)) g (by simpa [eq_to_hom_map] using w.symm)
 #align category_theory.structured_arrow.iso_mk CategoryTheory.StructuredArrow.isoMk
 
+#print CategoryTheory.StructuredArrow.ext /-
 theorem ext {A B : StructuredArrow S T} (f g : A ⟶ B) : f.right = g.right → f = g :=
   CommaMorphism.ext _ _ (Subsingleton.elim _ _)
 #align category_theory.structured_arrow.ext CategoryTheory.StructuredArrow.ext
+-/
 
+#print CategoryTheory.StructuredArrow.ext_iff /-
 theorem ext_iff {A B : StructuredArrow S T} (f g : A ⟶ B) : f = g ↔ f.right = g.right :=
   ⟨fun h => h ▸ rfl, ext f g⟩
 #align category_theory.structured_arrow.ext_iff CategoryTheory.StructuredArrow.ext_iff
+-/
 
+#print CategoryTheory.StructuredArrow.proj_faithful /-
 instance proj_faithful : Faithful (proj S T) where map_injective' X Y := ext
 #align category_theory.structured_arrow.proj_faithful CategoryTheory.StructuredArrow.proj_faithful
+-/
 
+#print CategoryTheory.StructuredArrow.mono_of_mono_right /-
 /-- The converse of this is true with additional assumptions, see `mono_iff_mono_right`. -/
 theorem mono_of_mono_right {A B : StructuredArrow S T} (f : A ⟶ B) [h : Mono f.right] : Mono f :=
   (proj S T).mono_of_mono_map h
 #align category_theory.structured_arrow.mono_of_mono_right CategoryTheory.StructuredArrow.mono_of_mono_right
+-/
 
+#print CategoryTheory.StructuredArrow.epi_of_epi_right /-
 theorem epi_of_epi_right {A B : StructuredArrow S T} (f : A ⟶ B) [h : Epi f.right] : Epi f :=
   (proj S T).epi_of_epi_map h
 #align category_theory.structured_arrow.epi_of_epi_right CategoryTheory.StructuredArrow.epi_of_epi_right
+-/
 
+/- warning: category_theory.structured_arrow.mono_hom_mk -> CategoryTheory.StructuredArrow.mono_homMk is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.mono_hom_mk CategoryTheory.StructuredArrow.mono_homMkₓ'. -/
 instance mono_homMk {A B : StructuredArrow S T} (f : A.right ⟶ B.right) (w) [h : Mono f] :
     Mono (homMk f w) :=
   (proj S T).mono_of_mono_map h
 #align category_theory.structured_arrow.mono_hom_mk CategoryTheory.StructuredArrow.mono_homMk
 
+/- warning: category_theory.structured_arrow.epi_hom_mk -> CategoryTheory.StructuredArrow.epi_homMk is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.epi_hom_mk CategoryTheory.StructuredArrow.epi_homMkₓ'. -/
 instance epi_homMk {A B : StructuredArrow S T} (f : A.right ⟶ B.right) (w) [h : Epi f] :
     Epi (homMk f w) :=
   (proj S T).epi_of_epi_map h
 #align category_theory.structured_arrow.epi_hom_mk CategoryTheory.StructuredArrow.epi_homMk
 
+#print CategoryTheory.StructuredArrow.eq_mk /-
 /-- Eta rule for structured arrows. Prefer `structured_arrow.eta`, since equality of objects tends
     to cause problems. -/
 theorem eq_mk (f : StructuredArrow S T) : f = mk f.Hom :=
@@ -147,13 +222,17 @@ theorem eq_mk (f : StructuredArrow S T) : f = mk f.Hom :=
   congr
   ext
 #align category_theory.structured_arrow.eq_mk CategoryTheory.StructuredArrow.eq_mk
+-/
 
+#print CategoryTheory.StructuredArrow.eta /-
 /-- Eta rule for structured arrows. -/
 @[simps]
 def eta (f : StructuredArrow S T) : f ≅ mk f.Hom :=
   isoMk (Iso.refl _) (by tidy)
 #align category_theory.structured_arrow.eta CategoryTheory.StructuredArrow.eta
+-/
 
+#print CategoryTheory.StructuredArrow.map /-
 /-- A morphism between source objects `S ⟶ S'`
 contravariantly induces a functor between structured arrows,
 `structured_arrow S' T ⥤ structured_arrow S T`.
@@ -166,12 +245,25 @@ to `Cat`.
 def map (f : S ⟶ S') : StructuredArrow S' T ⥤ StructuredArrow S T :=
   Comma.mapLeft _ ((Functor.const _).map f)
 #align category_theory.structured_arrow.map CategoryTheory.StructuredArrow.map
+-/
 
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 @[simp]
 theorem map_mk {f : S' ⟶ T.obj Y} (g : S ⟶ S') : (map g).obj (mk f) = mk (g ≫ f) :=
   rfl
 #align category_theory.structured_arrow.map_mk CategoryTheory.StructuredArrow.map_mk
 
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 @[simp]
 theorem map_id {f : StructuredArrow S T} : (map (𝟙 S)).obj f = f :=
   by
@@ -179,6 +271,12 @@ theorem map_id {f : StructuredArrow S T} : (map (𝟙 S)).obj f = f :=
   simp
 #align category_theory.structured_arrow.map_id CategoryTheory.StructuredArrow.map_id
 
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_inst_2 S'' T) (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S' T) (CategoryTheory.instCategoryStructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S' T) (CategoryTheory.StructuredArrow.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 S' S'' T f')) h))
+Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.map_comp CategoryTheory.StructuredArrow.map_compₓ'. -/
 @[simp]
 theorem map_comp {f : S ⟶ S'} {f' : S' ⟶ S''} {h : StructuredArrow S'' T} :
     (map (f ≫ f')).obj h = (map f).obj ((map f').obj h) :=
@@ -187,15 +285,23 @@ theorem map_comp {f : S ⟶ S'} {f' : S' ⟶ S''} {h : StructuredArrow S'' T} :
   simp
 #align category_theory.structured_arrow.map_comp CategoryTheory.StructuredArrow.map_comp
 
+#print CategoryTheory.StructuredArrow.proj_reflects_iso /-
 instance proj_reflects_iso : ReflectsIsomorphisms (proj S T)
     where reflects Y Z f t :=
     ⟨⟨structured_arrow.hom_mk (inv ((proj S T).map f)) (by simp), by tidy⟩⟩
 #align category_theory.structured_arrow.proj_reflects_iso CategoryTheory.StructuredArrow.proj_reflects_iso
+-/
 
 open CategoryTheory.Limits
 
 attribute [local tidy] tactic.discrete_cases
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.mk_id_initial CategoryTheory.StructuredArrow.mkIdInitialₓ'. -/
 /-- The identity structured arrow is initial. -/
 def mkIdInitial [Full T] [Faithful T] : IsInitial (mk (𝟙 (T.obj Y)))
     where
@@ -212,12 +318,20 @@ def mkIdInitial [Full T] [Faithful T] : IsInitial (mk (𝟙 (T.obj Y)))
 
 variable {A : Type u₃} [Category.{v₃} A] {B : Type u₄} [Category.{v₄} B]
 
+#print CategoryTheory.StructuredArrow.pre /-
 /-- The functor `(S, F ⋙ G) ⥤ (S, G)`. -/
 @[simps]
 def pre (S : D) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S (F ⋙ G) ⥤ StructuredArrow S G :=
   Comma.preRight _ F G
 #align category_theory.structured_arrow.pre CategoryTheory.StructuredArrow.pre
+-/
 
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+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} C] {D : Type.{u5}} [_inst_2 : CategoryTheory.Category.{u2, u5} D] {B : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} B] (S : C) (F : CategoryTheory.Functor.{u3, u1, u6, u4} B _inst_4 C _inst_1) (G : CategoryTheory.Functor.{u1, u2, u4, u5} C _inst_1 D _inst_2), CategoryTheory.Functor.{max u1 u3, max u2 u3, max u6 u1, max u6 u2} (CategoryTheory.StructuredArrow.{u3, u1, u6, u4} B _inst_4 C _inst_1 S F) (CategoryTheory.instCategoryStructuredArrow.{u3, u1, u6, u4} B _inst_4 C _inst_1 S F) (CategoryTheory.StructuredArrow.{u3, u2, u6, u5} B _inst_4 D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u4, u5} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u4} C (CategoryTheory.Category.toCategoryStruct.{u1, u4} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} D (CategoryTheory.Category.toCategoryStruct.{u2, u5} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u4, u5} C _inst_1 D _inst_2 G) S) (CategoryTheory.Functor.comp.{u3, u1, u2, u6, u4, u5} B _inst_4 C _inst_1 D _inst_2 F G)) (CategoryTheory.instCategoryStructuredArrow.{u3, u2, u6, u5} B _inst_4 D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u4, u5} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u4} C (CategoryTheory.Category.toCategoryStruct.{u1, u4} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u5} D (CategoryTheory.Category.toCategoryStruct.{u2, u5} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u4, u5} C _inst_1 D _inst_2 G) S) (CategoryTheory.Functor.comp.{u3, u1, u2, u6, u4, u5} B _inst_4 C _inst_1 D _inst_2 F G))
+Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.post CategoryTheory.StructuredArrow.postₓ'. -/
 /-- The functor `(S, F) ⥤ (G(S), F ⋙ G)`. -/
 @[simps]
 def post (S : C) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S F ⥤ StructuredArrow (G.obj S) (F ⋙ G)
@@ -226,6 +340,12 @@ def post (S : C) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S F ⥤ Structure
   map X Y f := StructuredArrow.homMk f.right (by simp [functor.comp_map, ← G.map_comp, ← f.w])
 #align category_theory.structured_arrow.post CategoryTheory.StructuredArrow.post
 
+/- warning: category_theory.structured_arrow.small_proj_preimage_of_locally_small -> CategoryTheory.StructuredArrow.small_proj_preimage_of_locallySmall is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] {S : D} {T : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2} {𝒢 : Set.{u3} C} [_inst_5 : Small.{u1, u3} (Set.Elem.{u3} C 𝒢)] [_inst_6 : CategoryTheory.LocallySmall.{u1, u2, u4} D _inst_2], Small.{u1, max u3 u2} (Set.Elem.{max u3 u2} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (Set.preimage.{max u3 u2, u3} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) C (Prefunctor.obj.{max (succ u1) (succ u2), succ u1, max u3 u2, u3} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max u3 u2} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max u3 u2} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.instCategoryStructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{max u1 u2, u1, max u3 u2, u3} (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.instCategoryStructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) C _inst_1 (CategoryTheory.StructuredArrow.proj.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T))) 𝒢))
+Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow.small_proj_preimage_of_locally_small CategoryTheory.StructuredArrow.small_proj_preimage_of_locallySmallₓ'. -/
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) :=
   by
@@ -238,6 +358,7 @@ instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢]
 
 end StructuredArrow
 
+#print CategoryTheory.CostructuredArrow /-
 /-- The category of `S`-costructured arrows with target `T : D` (here `S : C ⥤ D`),
 has as its objects `D`-morphisms of the form `S Y ⟶ T`, for some `Y : C`,
 and morphisms `C`-morphisms `Y ⟶ Y'` making the obvious triangle commute.
@@ -246,41 +367,80 @@ and morphisms `C`-morphisms `Y ⟶ Y'` making the obvious triangle commute.
 def CostructuredArrow (S : C ⥤ D) (T : D) :=
   Comma S (Functor.fromPUnit T)deriving Category
 #align category_theory.costructured_arrow CategoryTheory.CostructuredArrow
+-/
 
 namespace CostructuredArrow
 
+#print CategoryTheory.CostructuredArrow.proj /-
 /-- The obvious projection functor from costructured arrows. -/
 @[simps]
 def proj (S : C ⥤ D) (T : D) : CostructuredArrow S T ⥤ C :=
   Comma.fst _ _
 #align category_theory.costructured_arrow.proj CategoryTheory.CostructuredArrow.proj
+-/
 
 variable {T T' T'' : D} {Y Y' : C} {S : C ⥤ D}
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.mk CategoryTheory.CostructuredArrow.mkₓ'. -/
 /-- Construct a costructured arrow from a morphism. -/
 def mk (f : S.obj Y ⟶ T) : CostructuredArrow S T :=
   ⟨Y, ⟨⟨⟩⟩, f⟩
 #align category_theory.costructured_arrow.mk CategoryTheory.CostructuredArrow.mk
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.mk_left CategoryTheory.CostructuredArrow.mk_leftₓ'. -/
 @[simp]
 theorem mk_left (f : S.obj Y ⟶ T) : (mk f).left = Y :=
   rfl
 #align category_theory.costructured_arrow.mk_left CategoryTheory.CostructuredArrow.mk_left
 
+/- warning: category_theory.costructured_arrow.mk_right -> CategoryTheory.CostructuredArrow.mk_right is a dubious translation:
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 @[simp]
 theorem mk_right (f : S.obj Y ⟶ T) : (mk f).right = ⟨⟨⟩⟩ :=
   rfl
 #align category_theory.costructured_arrow.mk_right CategoryTheory.CostructuredArrow.mk_right
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.mk_hom_eq_self CategoryTheory.CostructuredArrow.mk_hom_eq_selfₓ'. -/
 @[simp]
 theorem mk_hom_eq_self (f : S.obj Y ⟶ T) : (mk f).Hom = f :=
   rfl
 #align category_theory.costructured_arrow.mk_hom_eq_self CategoryTheory.CostructuredArrow.mk_hom_eq_self
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.w CategoryTheory.CostructuredArrow.wₓ'. -/
 @[simp, reassoc.1]
 theorem w {A B : CostructuredArrow S T} (f : A ⟶ B) : S.map f.left ≫ B.Hom = A.Hom := by tidy
 #align category_theory.costructured_arrow.w CategoryTheory.CostructuredArrow.w
 
+/- warning: category_theory.costructured_arrow.hom_mk -> CategoryTheory.CostructuredArrow.homMk is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.hom_mk CategoryTheory.CostructuredArrow.homMkₓ'. -/
 /-- To construct a morphism of costructured arrows,
 we need a morphism of the objects underlying the source,
 and to check that the triangle commutes.
@@ -293,6 +453,12 @@ def homMk {f f' : CostructuredArrow S T} (g : f.left ⟶ f'.left) (w : S.map g 
   w' := by simpa [eq_to_hom_map] using w
 #align category_theory.costructured_arrow.hom_mk CategoryTheory.CostructuredArrow.homMk
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.iso_mk CategoryTheory.CostructuredArrow.isoMkₓ'. -/
 /-- To construct an isomorphism of costructured arrows,
 we need an isomorphism of the objects underlying the source,
 and to check that the triangle commutes.
@@ -303,36 +469,59 @@ def isoMk {f f' : CostructuredArrow S T} (g : f.left ≅ f'.left) (w : S.map g.H
   Comma.isoMk g (eqToIso (by ext)) (by simpa [eq_to_hom_map] using w)
 #align category_theory.costructured_arrow.iso_mk CategoryTheory.CostructuredArrow.isoMk
 
+#print CategoryTheory.CostructuredArrow.ext /-
 theorem ext {A B : CostructuredArrow S T} (f g : A ⟶ B) (h : f.left = g.left) : f = g :=
   CommaMorphism.ext _ _ h (Subsingleton.elim _ _)
 #align category_theory.costructured_arrow.ext CategoryTheory.CostructuredArrow.ext
+-/
 
+#print CategoryTheory.CostructuredArrow.ext_iff /-
 theorem ext_iff {A B : CostructuredArrow S T} (f g : A ⟶ B) : f = g ↔ f.left = g.left :=
   ⟨fun h => h ▸ rfl, ext f g⟩
 #align category_theory.costructured_arrow.ext_iff CategoryTheory.CostructuredArrow.ext_iff
+-/
 
+#print CategoryTheory.CostructuredArrow.proj_faithful /-
 instance proj_faithful : Faithful (proj S T) where map_injective' X Y := ext
 #align category_theory.costructured_arrow.proj_faithful CategoryTheory.CostructuredArrow.proj_faithful
+-/
 
+#print CategoryTheory.CostructuredArrow.mono_of_mono_left /-
 theorem mono_of_mono_left {A B : CostructuredArrow S T} (f : A ⟶ B) [h : Mono f.left] : Mono f :=
   (proj S T).mono_of_mono_map h
 #align category_theory.costructured_arrow.mono_of_mono_left CategoryTheory.CostructuredArrow.mono_of_mono_left
+-/
 
+#print CategoryTheory.CostructuredArrow.epi_of_epi_left /-
 /-- The converse of this is true with additional assumptions, see `epi_iff_epi_left`. -/
 theorem epi_of_epi_left {A B : CostructuredArrow S T} (f : A ⟶ B) [h : Epi f.left] : Epi f :=
   (proj S T).epi_of_epi_map h
 #align category_theory.costructured_arrow.epi_of_epi_left CategoryTheory.CostructuredArrow.epi_of_epi_left
+-/
 
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_inst_2 T S A B f w)
+Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.mono_hom_mk CategoryTheory.CostructuredArrow.mono_homMkₓ'. -/
 instance mono_homMk {A B : CostructuredArrow S T} (f : A.left ⟶ B.left) (w) [h : Mono f] :
     Mono (homMk f w) :=
   (proj S T).mono_of_mono_map h
 #align category_theory.costructured_arrow.mono_hom_mk CategoryTheory.CostructuredArrow.mono_homMk
 
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_inst_2 T S A B f w)
+Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.epi_hom_mk CategoryTheory.CostructuredArrow.epi_homMkₓ'. -/
 instance epi_homMk {A B : CostructuredArrow S T} (f : A.left ⟶ B.left) (w) [h : Epi f] :
     Epi (homMk f w) :=
   (proj S T).epi_of_epi_map h
 #align category_theory.costructured_arrow.epi_hom_mk CategoryTheory.CostructuredArrow.epi_homMk
 
+#print CategoryTheory.CostructuredArrow.eq_mk /-
 /-- Eta rule for costructured arrows. Prefer `costructured_arrow.eta`, as equality of objects tends
     to cause problems. -/
 theorem eq_mk (f : CostructuredArrow S T) : f = mk f.Hom :=
@@ -341,13 +530,17 @@ theorem eq_mk (f : CostructuredArrow S T) : f = mk f.Hom :=
   congr
   ext
 #align category_theory.costructured_arrow.eq_mk CategoryTheory.CostructuredArrow.eq_mk
+-/
 
+#print CategoryTheory.CostructuredArrow.eta /-
 /-- Eta rule for costructured arrows. -/
 @[simps]
 def eta (f : CostructuredArrow S T) : f ≅ mk f.Hom :=
   isoMk (Iso.refl _) (by tidy)
 #align category_theory.costructured_arrow.eta CategoryTheory.CostructuredArrow.eta
+-/
 
+#print CategoryTheory.CostructuredArrow.map /-
 /-- A morphism between target objects `T ⟶ T'`
 covariantly induces a functor between costructured arrows,
 `costructured_arrow S T ⥤ costructured_arrow S T'`.
@@ -360,12 +553,25 @@ to `Cat`.
 def map (f : T ⟶ T') : CostructuredArrow S T ⥤ CostructuredArrow S T' :=
   Comma.mapRight _ ((Functor.const _).map f)
 #align category_theory.costructured_arrow.map CategoryTheory.CostructuredArrow.map
+-/
 
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 @[simp]
 theorem map_mk {f : S.obj Y ⟶ T} (g : T ⟶ T') : (map g).obj (mk f) = mk (f ≫ g) :=
   rfl
 #align category_theory.costructured_arrow.map_mk CategoryTheory.CostructuredArrow.map_mk
 
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 @[simp]
 theorem map_id {f : CostructuredArrow S T} : (map (𝟙 T)).obj f = f :=
   by
@@ -373,6 +579,12 @@ theorem map_id {f : CostructuredArrow S T} : (map (𝟙 T)).obj f = f :=
   simp
 #align category_theory.costructured_arrow.map_id CategoryTheory.CostructuredArrow.map_id
 
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 @[simp]
 theorem map_comp {f : T ⟶ T'} {f' : T' ⟶ T''} {h : CostructuredArrow S T} :
     (map (f ≫ f')).obj h = (map f').obj ((map f).obj h) :=
@@ -381,15 +593,23 @@ theorem map_comp {f : T ⟶ T'} {f' : T' ⟶ T''} {h : CostructuredArrow S T} :
   simp
 #align category_theory.costructured_arrow.map_comp CategoryTheory.CostructuredArrow.map_comp
 
+#print CategoryTheory.CostructuredArrow.proj_reflects_iso /-
 instance proj_reflects_iso : ReflectsIsomorphisms (proj S T)
     where reflects Y Z f t :=
     ⟨⟨costructured_arrow.hom_mk (inv ((proj S T).map f)) (by simp), by tidy⟩⟩
 #align category_theory.costructured_arrow.proj_reflects_iso CategoryTheory.CostructuredArrow.proj_reflects_iso
+-/
 
 open CategoryTheory.Limits
 
 attribute [local tidy] tactic.discrete_cases
 
+/- warning: category_theory.costructured_arrow.mk_id_terminal -> CategoryTheory.CostructuredArrow.mkIdTerminal 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.costructured_arrow.mk_id_terminal CategoryTheory.CostructuredArrow.mkIdTerminalₓ'. -/
 /-- The identity costructured arrow is terminal. -/
 def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y)))
     where
@@ -407,12 +627,20 @@ def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y)))
 
 variable {A : Type u₃} [Category.{v₃} A] {B : Type u₄} [Category.{v₄} B]
 
+#print CategoryTheory.CostructuredArrow.pre /-
 /-- The functor `(F ⋙ G, S) ⥤ (G, S)`. -/
 @[simps]
 def pre (F : B ⥤ C) (G : C ⥤ D) (S : D) : CostructuredArrow (F ⋙ G) S ⥤ CostructuredArrow G S :=
   Comma.preLeft F G _
 #align category_theory.costructured_arrow.pre CategoryTheory.CostructuredArrow.pre
+-/
 
+/- warning: category_theory.costructured_arrow.post -> CategoryTheory.CostructuredArrow.post is a dubious translation:
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+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} C] {D : Type.{u5}} [_inst_2 : CategoryTheory.Category.{u2, u5} D] {B : Type.{u6}} [_inst_4 : CategoryTheory.Category.{u3, u6} B] (F : CategoryTheory.Functor.{u3, u1, u6, u4} B _inst_4 C _inst_1) (G : CategoryTheory.Functor.{u1, u2, u4, u5} C _inst_1 D _inst_2) (S : C), CategoryTheory.Functor.{max u3 u1, max u3 u2, max u6 u1, max u6 u2} (CategoryTheory.CostructuredArrow.{u3, u1, u6, u4} B _inst_4 C _inst_1 F S) (CategoryTheory.CostructuredArrow.category.{u1, u4, u6, u3} B _inst_4 C _inst_1 F S) (CategoryTheory.CostructuredArrow.{u3, u2, u6, u5} B _inst_4 D _inst_2 (CategoryTheory.Functor.comp.{u3, u1, u2, u6, u4, u5} B _inst_4 C _inst_1 D _inst_2 F G) (CategoryTheory.Functor.obj.{u1, u2, u4, u5} C _inst_1 D _inst_2 G S)) (CategoryTheory.CostructuredArrow.category.{u2, u5, u6, u3} B _inst_4 D _inst_2 (CategoryTheory.Functor.comp.{u3, u1, u2, u6, u4, u5} B _inst_4 C _inst_1 D _inst_2 F G) (CategoryTheory.Functor.obj.{u1, u2, u4, u5} C _inst_1 D _inst_2 G S))
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+Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.post CategoryTheory.CostructuredArrow.postₓ'. -/
 /-- The functor `(F, S) ⥤ (F ⋙ G, G(S))`. -/
 @[simps]
 def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :
@@ -422,6 +650,12 @@ def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :
   map X Y f := CostructuredArrow.homMk f.left (by simp [functor.comp_map, ← G.map_comp, ← f.w])
 #align category_theory.costructured_arrow.post CategoryTheory.CostructuredArrow.post
 
+/- warning: category_theory.costructured_arrow.small_proj_preimage_of_locally_small -> CategoryTheory.CostructuredArrow.small_proj_preimage_of_locallySmall is a dubious translation:
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+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] {T : D} {S : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2} {𝒢 : Set.{u3} C} [_inst_5 : Small.{u1, u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} C) Type.{u3} (Set.hasCoeToSort.{u3} C) 𝒢)] [_inst_6 : CategoryTheory.LocallySmall.{u1, u2, u4} D _inst_2], Small.{u1, max u3 u2} (coeSort.{succ (max u3 u2), succ (succ (max u3 u2))} (Set.{max u3 u2} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T)) Type.{max u3 u2} (Set.hasCoeToSort.{max u3 u2} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T)) (Set.preimage.{max u3 u2, u3} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) C (CategoryTheory.Functor.obj.{max u1 u2, u1, max u3 u2, u3} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T) (CategoryTheory.CostructuredArrow.category.{u2, u4, u3, u1} C _inst_1 D _inst_2 S T) C _inst_1 (CategoryTheory.CostructuredArrow.proj.{u1, u2, u3, u4} C _inst_1 D _inst_2 S T)) 𝒢))
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+Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow.small_proj_preimage_of_locally_small CategoryTheory.CostructuredArrow.small_proj_preimage_of_locallySmallₓ'. -/
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) :=
   by
@@ -438,6 +672,7 @@ open Opposite
 
 namespace StructuredArrow
 
+#print CategoryTheory.StructuredArrow.toCostructuredArrow /-
 /-- For a functor `F : C ⥤ D` and an object `d : D`, we obtain a contravariant functor from the
 category of structured arrows `d ⟶ F.obj c` to the category of costructured arrows
 `F.op.obj c ⟶ (op d)`.
@@ -454,7 +689,9 @@ def toCostructuredArrow (F : C ⥤ D) (d : D) :
         rw [← op_comp, ← f.unop.w, functor.const_obj_map]
         erw [category.id_comp])
 #align category_theory.structured_arrow.to_costructured_arrow CategoryTheory.StructuredArrow.toCostructuredArrow
+-/
 
+#print CategoryTheory.StructuredArrow.toCostructuredArrow' /-
 /-- For a functor `F : C ⥤ D` and an object `d : D`, we obtain a contravariant functor from the
 category of structured arrows `op d ⟶ F.op.obj c` to the category of costructured arrows
 `F.obj c ⟶ d`.
@@ -472,11 +709,13 @@ def toCostructuredArrow' (F : C ⥤ D) (d : D) :
           f.unop.w, functor.const_obj_map]
         erw [category.id_comp])
 #align category_theory.structured_arrow.to_costructured_arrow' CategoryTheory.StructuredArrow.toCostructuredArrow'
+-/
 
 end StructuredArrow
 
 namespace CostructuredArrow
 
+#print CategoryTheory.CostructuredArrow.toStructuredArrow /-
 /-- For a functor `F : C ⥤ D` and an object `d : D`, we obtain a contravariant functor from the
 category of costructured arrows `F.obj c ⟶ d` to the category of structured arrows
 `op d ⟶ F.op.obj c`.
@@ -492,7 +731,9 @@ def toStructuredArrow (F : C ⥤ D) (d : D) : (CostructuredArrow F d)ᵒᵖ ⥤
         rw [← op_comp, f.unop.w, functor.const_obj_map]
         erw [category.comp_id])
 #align category_theory.costructured_arrow.to_structured_arrow CategoryTheory.CostructuredArrow.toStructuredArrow
+-/
 
+#print CategoryTheory.CostructuredArrow.toStructuredArrow' /-
 /-- For a functor `F : C ⥤ D` and an object `d : D`, we obtain a contravariant functor from the
 category of costructured arrows `F.op.obj c ⟶ op d` to the category of structured arrows
 `d ⟶ F.obj c`.
@@ -509,9 +750,16 @@ def toStructuredArrow' (F : C ⥤ D) (d : D) : (CostructuredArrow F.op (op d))
           functor.const_obj_map]
         erw [category.comp_id])
 #align category_theory.costructured_arrow.to_structured_arrow' CategoryTheory.CostructuredArrow.toStructuredArrow'
+-/
 
 end CostructuredArrow
 
+/- warning: category_theory.structured_arrow_op_equivalence -> CategoryTheory.structuredArrowOpEquivalence is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.structured_arrow_op_equivalence CategoryTheory.structuredArrowOpEquivalenceₓ'. -/
 /-- For a functor `F : C ⥤ D` and an object `d : D`, the category of structured arrows `d ⟶ F.obj c`
 is contravariantly equivalent to the category of costructured arrows `F.op.obj c ⟶ op d`.
 -/
@@ -530,6 +778,12 @@ def structuredArrowOpEquivalence (F : C ⥤ D) (d : D) :
       fun X Y f => by ext; dsimp; simp)
 #align category_theory.structured_arrow_op_equivalence CategoryTheory.structuredArrowOpEquivalence
 
+/- warning: category_theory.costructured_arrow_op_equivalence -> CategoryTheory.costructuredArrowOpEquivalence is a dubious translation:
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+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (d : D), CategoryTheory.Equivalence.{max u1 u2, max u2 u1, max u3 u2, max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 F d)) (CategoryTheory.Category.opposite.{max u1 u2, max u3 u2} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 F d) (CategoryTheory.CostructuredArrow.category.{u2, u4, u3, u1} C _inst_1 D _inst_2 F d)) (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) (Opposite.{succ u4} D) (CategoryTheory.Category.opposite.{u2, u4} D _inst_2) (Opposite.op.{succ u4} D d) (CategoryTheory.Functor.op.{u1, u2, u3, u4} C _inst_1 D _inst_2 F)) (CategoryTheory.StructuredArrow.category.{u2, u4, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) (Opposite.{succ u4} D) (CategoryTheory.Category.opposite.{u2, u4} D _inst_2) (Opposite.op.{succ u4} D d) (CategoryTheory.Functor.op.{u1, u2, u3, u4} C _inst_1 D _inst_2 F))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (d : D), CategoryTheory.Equivalence.{max u1 u2, max u1 u2, max u3 u2, max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 F d)) (CategoryTheory.StructuredArrow.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) (Opposite.{succ u4} D) (CategoryTheory.Category.opposite.{u2, u4} D _inst_2) (Opposite.op.{succ u4} D d) (CategoryTheory.Functor.op.{u1, u2, u3, u4} C _inst_1 D _inst_2 F)) (CategoryTheory.Category.opposite.{max u1 u2, max u3 u2} (CategoryTheory.CostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 F d) (CategoryTheory.instCategoryCostructuredArrow.{u1, u2, u3, u4} C _inst_1 D _inst_2 F d)) (CategoryTheory.instCategoryStructuredArrow.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) (Opposite.{succ u4} D) (CategoryTheory.Category.opposite.{u2, u4} D _inst_2) (Opposite.op.{succ u4} D d) (CategoryTheory.Functor.op.{u1, u2, u3, u4} C _inst_1 D _inst_2 F))
+Case conversion may be inaccurate. Consider using '#align category_theory.costructured_arrow_op_equivalence CategoryTheory.costructuredArrowOpEquivalenceₓ'. -/
 /-- For a functor `F : C ⥤ D` and an object `d : D`, the category of costructured arrows
 `F.obj c ⟶ d` is contravariantly equivalent to the category of structured arrows
 `op d ⟶ F.op.obj c`.

bump to nightly-2023-02-28-22

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

1fb1623f

Diff

@@ -200,7 +200,7 @@ attribute [local tidy] tactic.discrete_cases
 def mkIdInitial [Full T] [Faithful T] : IsInitial (mk (𝟙 (T.obj Y)))
     where
   desc c :=
-    homMk (T.preimage c.x.Hom)
+    homMk (T.preimage c.pt.Hom)
       (by
         dsimp
         simp)
@@ -394,7 +394,7 @@ attribute [local tidy] tactic.discrete_cases
 def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y)))
     where
   lift c :=
-    homMk (S.preimage c.x.Hom)
+    homMk (S.preimage c.pt.Hom)
       (by
         dsimp
         simp)

bump to nightly-2023-02-27-08

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

91d8c210

Diff

@@ -204,7 +204,7 @@ def mkIdInitial [Full T] [Faithful T] : IsInitial (mk (𝟙 (T.obj Y)))
       (by
         dsimp
         simp)
-  uniq' c m _ := by
+  uniq c m _ := by
     ext
     apply T.map_injective
     simpa only [hom_mk_right, T.image_preimage, ← w m] using (category.id_comp _).symm
@@ -398,7 +398,7 @@ def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y)))
       (by
         dsimp
         simp)
-  uniq' := by
+  uniq := by
     rintro c m -
     ext
     apply S.map_injective

bump to nightly-2023-02-24-03

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

2d8bd121

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz, Scott Morrison
 
 ! This file was ported from Lean 3 source module category_theory.structured_arrow
-! leanprover-community/mathlib commit fef8efdf78f223294c34a41875923ab1272322d4
+! leanprover-community/mathlib commit 8a318021995877a44630c898d0b2bc376fceef3b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -94,7 +94,9 @@ def homMk {f f' : StructuredArrow S T} (g : f.right ⟶ f'.right) (w : f.Hom ≫
 structured arrow given by `(X ⟶ F(U)) ⟶ (X ⟶ F(U) ⟶ F(Y))`.
 -/
 def homMk' {F : C ⥤ D} {X : D} {Y : C} (U : StructuredArrow X F) (f : U.right ⟶ Y) :
-    U ⟶ mk (U.Hom ≫ F.map f) where right := f
+    U ⟶ mk (U.Hom ≫ F.map f) where
+  left := eqToHom (by ext)
+  right := f
 #align category_theory.structured_arrow.hom_mk' CategoryTheory.StructuredArrow.homMk'
 
 /-- To construct an isomorphism of structured arrows,
@@ -220,12 +222,8 @@ def pre (S : D) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S (F ⋙ G) ⥤ St
 @[simps]
 def post (S : C) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S F ⥤ StructuredArrow (G.obj S) (F ⋙ G)
     where
-  obj X :=
-    { right := X.right
-      Hom := G.map X.Hom }
-  map X Y f :=
-    { right := f.right
-      w' := by simp [functor.comp_map, ← G.map_comp, ← f.w] }
+  obj X := StructuredArrow.mk (G.map X.Hom)
+  map X Y f := StructuredArrow.homMk f.right (by simp [functor.comp_map, ← G.map_comp, ← f.w])
 #align category_theory.structured_arrow.post CategoryTheory.StructuredArrow.post
 
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
@@ -420,12 +418,8 @@ def pre (F : B ⥤ C) (G : C ⥤ D) (S : D) : CostructuredArrow (F ⋙ G) S ⥤
 def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :
     CostructuredArrow F S ⥤ CostructuredArrow (F ⋙ G) (G.obj S)
     where
-  obj X :=
-    { left := X.left
-      Hom := G.map X.Hom }
-  map X Y f :=
-    { left := f.left
-      w' := by simp [functor.comp_map, ← G.map_comp, ← f.w] }
+  obj X := CostructuredArrow.mk (G.map X.Hom)
+  map X Y f := CostructuredArrow.homMk f.left (by simp [functor.comp_map, ← G.map_comp, ← f.w])
 #align category_theory.costructured_arrow.post CategoryTheory.CostructuredArrow.post
 
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :

bump to nightly-2023-02-21-20

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

7f7a4bc1

Diff

@@ -38,7 +38,7 @@ and morphisms `C`-morphisms `Y ⟶ Y'` making the obvious triangle commute.
 -/
 @[nolint has_nonempty_instance]
 def StructuredArrow (S : D) (T : C ⥤ D) :=
-  Comma (Functor.fromPunit S) T deriving Category
+  Comma (Functor.fromPUnit S) T deriving Category
 #align category_theory.structured_arrow CategoryTheory.StructuredArrow
 
 namespace StructuredArrow
@@ -246,7 +246,7 @@ and morphisms `C`-morphisms `Y ⟶ Y'` making the obvious triangle commute.
 -/
 @[nolint has_nonempty_instance]
 def CostructuredArrow (S : C ⥤ D) (T : D) :=
-  Comma S (Functor.fromPunit T)deriving Category
+  Comma S (Functor.fromPUnit T)deriving Category
 #align category_theory.costructured_arrow CategoryTheory.CostructuredArrow
 
 namespace CostructuredArrow

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore(CategoryTheory): make Functor.Full a Prop (#12449)

Before this PR, Functor.Full contained the data of the preimage of maps by a full functor F. This PR makes Functor.Full a proposition. This is to prevent any diamond to appear.

The lemma Functor.image_preimage is also renamed Functor.map_preimage.

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

ce289a0e

Diff

@@ -275,7 +275,7 @@ instance proj_reflectsIsomorphisms : (proj S T).ReflectsIsomorphisms where
 open CategoryTheory.Limits
 
 /-- The identity structured arrow is initial. -/
-def mkIdInitial [T.Full] [T.Faithful] : IsInitial (mk (𝟙 (T.obj Y))) where
+noncomputable def mkIdInitial [T.Full] [T.Faithful] : IsInitial (mk (𝟙 (T.obj Y))) where
   desc c := homMk (T.preimage c.pt.hom)
   uniq c m _ := by
     apply CommaMorphism.ext
@@ -318,7 +318,7 @@ instance (S : C) (F : B ⥤ C) (G : C ⥤ D) : (post S F G).Faithful where
   map_injective {_ _} _ _ h := by simpa [ext_iff] using h
 
 instance (S : C) (F : B ⥤ C) (G : C ⥤ D) [G.Faithful] : (post S F G).Full where
-  preimage {_ _} f := homMk f.right (G.map_injective (by simpa using f.w.symm))
+  map_surjective f := ⟨homMk f.right (G.map_injective (by simpa using f.w.symm)), by aesop_cat⟩
 
 instance (S : C) (F : B ⥤ C) (G : C ⥤ D) [G.Full] : (post S F G).EssSurj where
   mem_essImage h := ⟨mk (G.preimage h.hom), ⟨isoMk (Iso.refl _) (by simp)⟩⟩
@@ -613,7 +613,7 @@ instance proj_reflectsIsomorphisms : (proj S T).ReflectsIsomorphisms where
 open CategoryTheory.Limits
 
 /-- The identity costructured arrow is terminal. -/
-def mkIdTerminal [S.Full] [S.Faithful] : IsTerminal (mk (𝟙 (S.obj Y))) where
+noncomputable def mkIdTerminal [S.Full] [S.Faithful] : IsTerminal (mk (𝟙 (S.obj Y))) where
   lift c := homMk (S.preimage c.pt.hom)
   uniq := by
     rintro c m -
@@ -656,7 +656,7 @@ instance (F : B ⥤ C) (G : C ⥤ D) (S : C) : (post F G S).Faithful where
   map_injective {_ _} _ _ h := by simpa [ext_iff] using h
 
 instance (F : B ⥤ C) (G : C ⥤ D) (S : C) [G.Faithful] : (post F G S).Full where
-  preimage {_ _} f := homMk f.left (G.map_injective (by simpa using f.w))
+  map_surjective f := ⟨homMk f.left (G.map_injective (by simpa using f.w)), by aesop_cat⟩
 
 instance (F : B ⥤ C) (G : C ⥤ D) (S : C) [G.Full] : (post F G S).EssSurj where
   mem_essImage h := ⟨mk (G.preimage h.hom), ⟨isoMk (Iso.refl _) (by simp)⟩⟩

chore: classify porting notes referring to missing linters (#12098)

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.

c5b5490c

Diff

@@ -36,6 +36,7 @@ and morphisms `C`-morphisms `Y ⟶ Y'` making the obvious triangle commute.
 -/
 -- We explicitly come from `PUnit.{1}` here to obtain the correct universe for morphisms of
 -- structured arrows.
+-- Porting note(#5171): linter not ported yet
 -- @[nolint has_nonempty_instance]
 def StructuredArrow (S : D) (T : C ⥤ D) :=
   Comma (Functor.fromPUnit.{0} S) T
@@ -380,7 +381,7 @@ and morphisms `C`-morphisms `Y ⟶ Y'` making the obvious triangle commute.
 -/
 -- We explicitly come from `PUnit.{1}` here to obtain the correct universe for morphisms of
 -- costructured arrows.
--- @[nolint has_nonempty_instance] -- Porting note: removed
+-- @[nolint has_nonempty_instance] -- Porting note(#5171): linter not ported yet
 def CostructuredArrow (S : C ⥤ D) (T : D) :=
   Comma S (Functor.fromPUnit.{0} T)
 #align category_theory.costructured_arrow CategoryTheory.CostructuredArrow

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

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

65b7affc

Diff

@@ -182,7 +182,7 @@ theorem ext_iff {A B : StructuredArrow S T} (f g : A ⟶ B) : f = g ↔ f.right
   ⟨fun h => h ▸ rfl, ext f g⟩
 #align category_theory.structured_arrow.ext_iff CategoryTheory.StructuredArrow.ext_iff
 
-instance proj_faithful : Faithful (proj S T) where
+instance proj_faithful : (proj S T).Faithful where
   map_injective {_ _} := ext
 #align category_theory.structured_arrow.proj_faithful CategoryTheory.StructuredArrow.proj_faithful
 
@@ -263,7 +263,7 @@ def mapIso (i : S ≅ S') : StructuredArrow S T ≌ StructuredArrow S' T :=
 def mapNatIso (i : T ≅ T') : StructuredArrow S T ≌ StructuredArrow S T' :=
   Comma.mapRightIso _ i
 
-instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T) where
+instance proj_reflectsIsomorphisms : (proj S T).ReflectsIsomorphisms where
   reflects {Y Z} f t :=
     ⟨⟨StructuredArrow.homMk
         (inv ((proj S T).map f))
@@ -274,7 +274,7 @@ instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T) where
 open CategoryTheory.Limits
 
 /-- The identity structured arrow is initial. -/
-def mkIdInitial [Full T] [Faithful T] : IsInitial (mk (𝟙 (T.obj Y))) where
+def mkIdInitial [T.Full] [T.Faithful] : IsInitial (mk (𝟙 (T.obj Y))) where
   desc c := homMk (T.preimage c.pt.hom)
   uniq c m _ := by
     apply CommaMorphism.ext
@@ -291,18 +291,18 @@ def pre (S : D) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S (F ⋙ G) ⥤ St
   Comma.preRight _ F G
 #align category_theory.structured_arrow.pre CategoryTheory.StructuredArrow.pre
 
-instance (S : D) (F : B ⥤ C) (G : C ⥤ D) [Faithful F] : Faithful (pre S F G) :=
-  show Faithful (Comma.preRight _ _ _) from inferInstance
+instance (S : D) (F : B ⥤ C) (G : C ⥤ D) [F.Faithful] : (pre S F G).Faithful :=
+  show (Comma.preRight _ _ _).Faithful from inferInstance
 
-instance (S : D) (F : B ⥤ C) (G : C ⥤ D) [Full F] : Full (pre S F G) :=
-  show Full (Comma.preRight _ _ _) from inferInstance
+instance (S : D) (F : B ⥤ C) (G : C ⥤ D) [F.Full] : (pre S F G).Full :=
+  show (Comma.preRight _ _ _).Full from inferInstance
 
-instance (S : D) (F : B ⥤ C) (G : C ⥤ D) [EssSurj F] : EssSurj (pre S F G) :=
-  show EssSurj (Comma.preRight _ _ _) from inferInstance
+instance (S : D) (F : B ⥤ C) (G : C ⥤ D) [F.EssSurj] : (pre S F G).EssSurj :=
+  show (Comma.preRight _ _ _).EssSurj from inferInstance
 
 /-- If `F` is an equivalence, then so is the functor `(S, F ⋙ G) ⥤ (S, G)`. -/
-noncomputable def isEquivalencePre (S : D) (F : B ⥤ C) (G : C ⥤ D) [IsEquivalence F] :
-    IsEquivalence (pre S F G) :=
+noncomputable def isEquivalencePre (S : D) (F : B ⥤ C) (G : C ⥤ D) [F.IsEquivalence] :
+    (pre S F G).IsEquivalence :=
   Comma.isEquivalencePreRight _ _ _
 
 /-- The functor `(S, F) ⥤ (G(S), F ⋙ G)`. -/
@@ -313,19 +313,19 @@ def post (S : C) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S F ⥤ Structure
   map f := StructuredArrow.homMk f.right (by simp [Functor.comp_map, ← G.map_comp, ← f.w])
 #align category_theory.structured_arrow.post CategoryTheory.StructuredArrow.post
 
-instance (S : C) (F : B ⥤ C) (G : C ⥤ D) : Faithful (post S F G) where
+instance (S : C) (F : B ⥤ C) (G : C ⥤ D) : (post S F G).Faithful where
   map_injective {_ _} _ _ h := by simpa [ext_iff] using h
 
-instance (S : C) (F : B ⥤ C) (G : C ⥤ D) [Faithful G] : Full (post S F G) where
+instance (S : C) (F : B ⥤ C) (G : C ⥤ D) [G.Faithful] : (post S F G).Full where
   preimage {_ _} f := homMk f.right (G.map_injective (by simpa using f.w.symm))
 
-instance (S : C) (F : B ⥤ C) (G : C ⥤ D) [Full G] : EssSurj (post S F G) where
+instance (S : C) (F : B ⥤ C) (G : C ⥤ D) [G.Full] : (post S F G).EssSurj where
   mem_essImage h := ⟨mk (G.preimage h.hom), ⟨isoMk (Iso.refl _) (by simp)⟩⟩
 
 /-- If `G` is fully faithful, then `post S F G : (S, F) ⥤ (G(S), F ⋙ G)` is an equivalence. -/
-noncomputable def isEquivalencePost (S : C) (F : B ⥤ C) (G : C ⥤ D) [Full G] [Faithful G] :
-    IsEquivalence (post S F G) :=
-  Equivalence.ofFullyFaithfullyEssSurj _
+noncomputable def isEquivalencePost (S : C) (F : B ⥤ C) (G : C ⥤ D) [G.Full] [G.Faithful] :
+    (post S F G).IsEquivalence :=
+  Functor.IsEquivalence.ofFullyFaithfullyEssSurj _
 
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) := by
@@ -520,7 +520,7 @@ theorem ext_iff {A B : CostructuredArrow S T} (f g : A ⟶ B) : f = g ↔ f.left
   ⟨fun h => h ▸ rfl, ext f g⟩
 #align category_theory.costructured_arrow.ext_iff CategoryTheory.CostructuredArrow.ext_iff
 
-instance proj_faithful : Faithful (proj S T) where map_injective {_ _} := ext
+instance proj_faithful : (proj S T).Faithful where map_injective {_ _} := ext
 #align category_theory.costructured_arrow.proj_faithful CategoryTheory.CostructuredArrow.proj_faithful
 
 theorem mono_of_mono_left {A B : CostructuredArrow S T} (f : A ⟶ B) [h : Mono f.left] : Mono f :=
@@ -601,7 +601,7 @@ def mapIso (i : T ≅ T') : CostructuredArrow S T ≌ CostructuredArrow S T' :=
 def mapNatIso (i : S ≅ S') : CostructuredArrow S T ≌ CostructuredArrow S' T :=
   Comma.mapLeftIso _ i
 
-instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T) where
+instance proj_reflectsIsomorphisms : (proj S T).ReflectsIsomorphisms where
   reflects {Y Z} f t :=
     ⟨⟨CostructuredArrow.homMk
         (inv ((proj S T).map f))
@@ -612,7 +612,7 @@ instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T) where
 open CategoryTheory.Limits
 
 /-- The identity costructured arrow is terminal. -/
-def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y))) where
+def mkIdTerminal [S.Full] [S.Faithful] : IsTerminal (mk (𝟙 (S.obj Y))) where
   lift c := homMk (S.preimage c.pt.hom)
   uniq := by
     rintro c m -
@@ -629,18 +629,18 @@ def pre (F : B ⥤ C) (G : C ⥤ D) (S : D) : CostructuredArrow (F ⋙ G) S ⥤
   Comma.preLeft F G _
 #align category_theory.costructured_arrow.pre CategoryTheory.CostructuredArrow.pre
 
-instance (F : B ⥤ C) (G : C ⥤ D) (S : D) [Faithful F] : Faithful (pre F G S) :=
-  show Faithful (Comma.preLeft _ _ _) from inferInstance
+instance (F : B ⥤ C) (G : C ⥤ D) (S : D) [F.Faithful] : (pre F G S).Faithful :=
+  show (Comma.preLeft _ _ _).Faithful from inferInstance
 
-instance (F : B ⥤ C) (G : C ⥤ D) (S : D) [Full F] : Full (pre F G S) :=
-  show Full (Comma.preLeft _ _ _) from inferInstance
+instance (F : B ⥤ C) (G : C ⥤ D) (S : D) [F.Full] : (pre F G S).Full :=
+  show (Comma.preLeft _ _ _).Full from inferInstance
 
-instance (F : B ⥤ C) (G : C ⥤ D) (S : D) [EssSurj F] : EssSurj (pre F G S) :=
-  show EssSurj (Comma.preLeft _ _ _) from inferInstance
+instance (F : B ⥤ C) (G : C ⥤ D) (S : D) [F.EssSurj] : (pre F G S).EssSurj :=
+  show (Comma.preLeft _ _ _).EssSurj from inferInstance
 
 /-- If `F` is an equivalence, then so is the functor `(F ⋙ G, S) ⥤ (G, S)`. -/
-noncomputable def isEquivalencePre (F : B ⥤ C) (G : C ⥤ D) (S : D) [IsEquivalence F] :
-    IsEquivalence (pre F G S) :=
+noncomputable def isEquivalencePre (F : B ⥤ C) (G : C ⥤ D) (S : D) [F.IsEquivalence] :
+    (pre F G S).IsEquivalence :=
   Comma.isEquivalencePreLeft _ _ _
 
 /-- The functor `(F, S) ⥤ (F ⋙ G, G(S))`. -/
@@ -651,19 +651,19 @@ def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :
   map f := CostructuredArrow.homMk f.left (by simp [Functor.comp_map, ← G.map_comp, ← f.w])
 #align category_theory.costructured_arrow.post CategoryTheory.CostructuredArrow.post
 
-instance (F : B ⥤ C) (G : C ⥤ D) (S : C) : Faithful (post F G S) where
+instance (F : B ⥤ C) (G : C ⥤ D) (S : C) : (post F G S).Faithful where
   map_injective {_ _} _ _ h := by simpa [ext_iff] using h
 
-instance (F : B ⥤ C) (G : C ⥤ D) (S : C) [Faithful G] : Full (post F G S) where
+instance (F : B ⥤ C) (G : C ⥤ D) (S : C) [G.Faithful] : (post F G S).Full where
   preimage {_ _} f := homMk f.left (G.map_injective (by simpa using f.w))
 
-instance (F : B ⥤ C) (G : C ⥤ D) (S : C) [Full G] : EssSurj (post F G S) where
+instance (F : B ⥤ C) (G : C ⥤ D) (S : C) [G.Full] : (post F G S).EssSurj where
   mem_essImage h := ⟨mk (G.preimage h.hom), ⟨isoMk (Iso.refl _) (by simp)⟩⟩
 
 /-- If `G` is fully faithful, then `post F G S : (F, S) ⥤ (F ⋙ G, G(S))` is an equivalence. -/
-noncomputable def isEquivalencePost (S : C) (F : B ⥤ C) (G : C ⥤ D) [Full G] [Faithful G] :
-    IsEquivalence (post F G S) :=
-  Equivalence.ofFullyFaithfullyEssSurj _
+noncomputable def isEquivalencePost (S : C) (F : B ⥤ C) (G : C ⥤ D) [G.Full] [G.Faithful] :
+    (post F G S).IsEquivalence :=
+  Functor.IsEquivalence.ofFullyFaithfullyEssSurj _
 
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) := by

style: replace '.-/' by '. -/' (#11938)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

3556ded2

Diff

@@ -258,7 +258,7 @@ def mapIso (i : S ≅ S') : StructuredArrow S T ≌ StructuredArrow S' T :=
   Comma.mapLeftIso _ ((Functor.const _).mapIso i)
 
 /-- A natural isomorphism `T ≅ T'` induces an equivalence
-    `StructuredArrow S T ≌ StructuredArrow S T'`.-/
+    `StructuredArrow S T ≌ StructuredArrow S T'`. -/
 @[simp]
 def mapNatIso (i : T ≅ T') : StructuredArrow S T ≌ StructuredArrow S T' :=
   Comma.mapRightIso _ i

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

8be0b69c

Diff

@@ -54,7 +54,7 @@ def proj (S : D) (T : C ⥤ D) : StructuredArrow S T ⥤ C :=
 
 variable {S S' S'' : D} {Y Y' Y'' : C} {T T' : C ⥤ D}
 
--- porting note: this lemma was added because `Comma.hom_ext`
+-- Porting note: this lemma was added because `Comma.hom_ext`
 -- was not triggered automatically
 -- See https://github.com/leanprover-community/mathlib4/issues/5229
 @[ext]
@@ -397,7 +397,7 @@ def proj (S : C ⥤ D) (T : D) : CostructuredArrow S T ⥤ C :=
 
 variable {T T' T'' : D} {Y Y' Y'' : C} {S S' : C ⥤ D}
 
--- porting note: this lemma was added because `Comma.hom_ext`
+-- Porting note: this lemma was added because `Comma.hom_ext`
 -- was not triggered automatically
 -- See https://github.com/leanprover-community/mathlib4/issues/5229
 @[ext]

feat: small_iUnion and small_sUnion (#10921)

Also moves the other results about Small on sets to their own file.

89415b39

Diff

@@ -7,6 +7,7 @@ import Mathlib.CategoryTheory.Comma.Basic
 import Mathlib.CategoryTheory.PUnit
 import Mathlib.CategoryTheory.Limits.Shapes.Terminal
 import Mathlib.CategoryTheory.EssentiallySmall
+import Mathlib.Logic.Small.Set
 
 #align_import category_theory.structured_arrow from "leanprover-community/mathlib"@"8a318021995877a44630c898d0b2bc376fceef3b"

style: reduce spacing variation in "porting note" comments (#10886)

In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.

86b84c52

Diff

@@ -119,7 +119,7 @@ def homMk {f f' : StructuredArrow S T} (g : f.right ⟶ f'.right)
     simpa using w.symm
 #align category_theory.structured_arrow.hom_mk CategoryTheory.StructuredArrow.homMk
 
-/- Porting note : it appears the simp lemma is not getting generated but the linter
+/- Porting note: it appears the simp lemma is not getting generated but the linter
 picks up on it (seems like a bug). Either way simp solves it.  -/
 attribute [-simp, nolint simpNF] homMk_left
 
@@ -169,7 +169,7 @@ def isoMk {f f' : StructuredArrow S T} (g : f.right ≅ f'.right)
   Comma.isoMk (eqToIso (by ext)) g (by simpa using w.symm)
 #align category_theory.structured_arrow.iso_mk CategoryTheory.StructuredArrow.isoMk
 
-/- Porting note : it appears the simp lemma is not getting generated but the linter
+/- Porting note: it appears the simp lemma is not getting generated but the linter
 picks up on it. Either way simp solves these. -/
 attribute [-simp, nolint simpNF] isoMk_hom_left_down_down isoMk_inv_left_down_down
 
@@ -216,7 +216,7 @@ def eta (f : StructuredArrow S T) : f ≅ mk f.hom :=
   isoMk (Iso.refl _)
 #align category_theory.structured_arrow.eta CategoryTheory.StructuredArrow.eta
 
-/- Porting note : it appears the simp lemma is not getting generated but the linter
+/- Porting note: it appears the simp lemma is not getting generated but the linter
 picks up on it. Either way simp solves these. -/
 attribute [-simp, nolint simpNF] eta_hom_left_down_down eta_inv_left_down_down
 
@@ -507,7 +507,7 @@ def isoMk {f f' : CostructuredArrow S T} (g : f.left ≅ f'.left)
   Comma.isoMk g (eqToIso (by ext)) (by simpa using w)
 #align category_theory.costructured_arrow.iso_mk CategoryTheory.CostructuredArrow.isoMk
 
-/- Porting note : it appears the simp lemma is not getting generated but the linter
+/- Porting note: it appears the simp lemma is not getting generated but the linter
 picks up on it. Either way simp solves these. -/
 attribute [-simp, nolint simpNF] isoMk_hom_right_down_down isoMk_inv_right_down_down
 
@@ -553,7 +553,7 @@ def eta (f : CostructuredArrow S T) : f ≅ mk f.hom :=
   isoMk (Iso.refl _)
 #align category_theory.costructured_arrow.eta CategoryTheory.CostructuredArrow.eta
 
-/- Porting note : it appears the simp lemma is not getting generated but the linter
+/- Porting note: it appears the simp lemma is not getting generated but the linter
 picks up on it. Either way simp solves these. -/
 attribute [-simp, nolint simpNF] eta_hom_right_down_down eta_inv_right_down_down

chore: classify simp can do this porting notes (#10619)

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

de765f60

Diff

@@ -459,7 +459,7 @@ def homMk {f f' : CostructuredArrow S T} (g : f.left ⟶ f'.left)
   right := 𝟙 _
 #align category_theory.costructured_arrow.hom_mk CategoryTheory.CostructuredArrow.homMk
 
-/- Porting note : it appears the simp lemma is not getting generated but the linter
+/- Porting note: it appears the simp lemma is not getting generated but the linter
 picks up on it. Either way simp can prove this -/
 attribute [-simp, nolint simpNF] homMk_right_down_down

feat: trivial morphisms in StructuredArrow (#10244)

6d4aa853

Diff

@@ -112,7 +112,7 @@ and to check that the triangle commutes.
 @[simps]
 def homMk {f f' : StructuredArrow S T} (g : f.right ⟶ f'.right)
     (w : f.hom ≫ T.map g = f'.hom := by aesop_cat) : f ⟶ f' where
-  left := eqToHom (by ext)
+  left := 𝟙 _
   right := g
   w := by
     dsimp
@@ -127,7 +127,7 @@ attribute [-simp, nolint simpNF] homMk_left
     structured arrows given by `(X ⟶ T(Y)) ⟶ (X ⟶ T(Y) ⟶ T(Y'))`.  -/
 @[simps]
 def homMk' (f : StructuredArrow S T) (g : f.right ⟶ Y') : f ⟶ mk (f.hom ≫ T.map g) where
-  left := eqToHom (by ext)
+  left := 𝟙 _
   right := g
 #align category_theory.structured_arrow.hom_mk' CategoryTheory.StructuredArrow.homMk'
 
@@ -147,6 +147,17 @@ lemma homMk'_mk_comp (f : S ⟶ T.obj Y) (g : Y ⟶ Y') (g' : Y' ⟶ Y'') :
     homMk' (mk f) (g ≫ g') = homMk' (mk f) g ≫ homMk' (mk (f ≫ T.map g)) g' ≫ eqToHom (by simp) :=
   homMk'_comp _ _ _
 
+/-- Variant of `homMk'` where both objects are applications of `mk`. -/
+@[simps]
+def mkPostcomp (f : S ⟶ T.obj Y) (g : Y ⟶ Y') : mk f ⟶ mk (f ≫ T.map g) where
+  left := 𝟙 _
+  right := g
+
+lemma mkPostcomp_id (f : S ⟶ T.obj Y) : mkPostcomp f (𝟙 Y) = eqToHom (by aesop_cat) := by aesop_cat
+lemma mkPostcomp_comp (f : S ⟶ T.obj Y) (g : Y ⟶ Y') (g' : Y' ⟶ Y'') :
+    mkPostcomp f (g ≫ g') = mkPostcomp f g ≫ mkPostcomp (f ≫ T.map g) g' ≫ eqToHom (by simp) := by
+  aesop_cat
+
 /-- To construct an isomorphism of structured arrows,
 we need an isomorphism of the objects underlying the target,
 and to check that the triangle commutes.
@@ -155,7 +166,7 @@ and to check that the triangle commutes.
 def isoMk {f f' : StructuredArrow S T} (g : f.right ≅ f'.right)
     (w : f.hom ≫ T.map g.hom = f'.hom := by aesop_cat) :
     f ≅ f' :=
-  Comma.isoMk (eqToIso (by ext)) g (by simpa [eqToHom_map] using w.symm)
+  Comma.isoMk (eqToIso (by ext)) g (by simpa using w.symm)
 #align category_theory.structured_arrow.iso_mk CategoryTheory.StructuredArrow.isoMk
 
 /- Porting note : it appears the simp lemma is not getting generated but the linter
@@ -445,8 +456,7 @@ and to check that the triangle commutes.
 def homMk {f f' : CostructuredArrow S T} (g : f.left ⟶ f'.left)
     (w : S.map g ≫ f'.hom = f.hom := by aesop_cat) : f ⟶ f' where
   left := g
-  right := eqToHom (by ext)
-  w := by simpa [eqToHom_map] using w
+  right := 𝟙 _
 #align category_theory.costructured_arrow.hom_mk CategoryTheory.CostructuredArrow.homMk
 
 /- Porting note : it appears the simp lemma is not getting generated but the linter
@@ -458,7 +468,7 @@ attribute [-simp, nolint simpNF] homMk_right_down_down
 @[simps]
 def homMk' (f : CostructuredArrow S T) (g : Y' ⟶ f.left) : mk (S.map g ≫ f.hom) ⟶ f where
   left := g
-  right := eqToHom (by ext)
+  right := 𝟙 _
 
 lemma homMk'_id (f : CostructuredArrow S T) : homMk' f (𝟙 f.left) = eqToHom (by aesop_cat) := by
   ext
@@ -476,6 +486,17 @@ lemma homMk'_mk_comp (f : S.obj Y ⟶ T) (g : Y' ⟶ Y) (g' : Y'' ⟶ Y') :
     homMk' (mk f) (g' ≫ g) = eqToHom (by simp) ≫ homMk' (mk (S.map g ≫ f)) g' ≫ homMk' (mk f) g :=
   homMk'_comp _ _ _
 
+/-- Variant of `homMk'` where both objects are applications of `mk`. -/
+@[simps]
+def mkPrecomp (f : S.obj Y ⟶ T) (g : Y' ⟶ Y) : mk (S.map g ≫ f) ⟶ mk f where
+  left := g
+  right := 𝟙 _
+
+lemma mkPrecomp_id (f : S.obj Y ⟶ T) : mkPrecomp f (𝟙 Y) = eqToHom (by aesop_cat) := by aesop_cat
+lemma mkPrecomp_comp (f : S.obj Y ⟶ T) (g : Y' ⟶ Y) (g' : Y'' ⟶ Y') :
+    mkPrecomp f (g' ≫ g) = eqToHom (by simp) ≫ mkPrecomp (S.map g ≫ f) g' ≫ mkPrecomp f g := by
+  aesop_cat
+
 /-- To construct an isomorphism of costructured arrows,
 we need an isomorphism of the objects underlying the source,
 and to check that the triangle commutes.
@@ -483,7 +504,7 @@ and to check that the triangle commutes.
 @[simps!]
 def isoMk {f f' : CostructuredArrow S T} (g : f.left ≅ f'.left)
     (w : S.map g.hom ≫ f'.hom = f.hom := by aesop_cat) : f ≅ f' :=
-  Comma.isoMk g (eqToIso (by ext)) (by simpa [eqToHom_map] using w)
+  Comma.isoMk g (eqToIso (by ext)) (by simpa using w)
 #align category_theory.costructured_arrow.iso_mk CategoryTheory.CostructuredArrow.isoMk
 
 /- Porting note : it appears the simp lemma is not getting generated but the linter

refactor: create folder CategoryTheory/Comma (#10108)

38cd7278

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz, Scott Morrison
 -/
+import Mathlib.CategoryTheory.Comma.Basic
 import Mathlib.CategoryTheory.PUnit
-import Mathlib.CategoryTheory.Comma
 import Mathlib.CategoryTheory.Limits.Shapes.Terminal
 import Mathlib.CategoryTheory.EssentiallySmall

chore: space after ← (#8178)

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

5fb9beab

Diff

@@ -298,7 +298,7 @@ noncomputable def isEquivalencePre (S : D) (F : B ⥤ C) (G : C ⥤ D) [IsEquiva
 def post (S : C) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S F ⥤ StructuredArrow (G.obj S) (F ⋙ G)
     where
   obj X := StructuredArrow.mk (G.map X.hom)
-  map f := StructuredArrow.homMk f.right (by simp [Functor.comp_map, ←G.map_comp, ← f.w])
+  map f := StructuredArrow.homMk f.right (by simp [Functor.comp_map, ← G.map_comp, ← f.w])
 #align category_theory.structured_arrow.post CategoryTheory.StructuredArrow.post
 
 instance (S : C) (F : B ⥤ C) (G : C ⥤ D) : Faithful (post S F G) where
@@ -626,7 +626,7 @@ noncomputable def isEquivalencePre (F : B ⥤ C) (G : C ⥤ D) (S : D) [IsEquiva
 def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :
     CostructuredArrow F S ⥤ CostructuredArrow (F ⋙ G) (G.obj S) where
   obj X := CostructuredArrow.mk (G.map X.hom)
-  map f := CostructuredArrow.homMk f.left (by simp [Functor.comp_map, ←G.map_comp, ← f.w])
+  map f := CostructuredArrow.homMk f.left (by simp [Functor.comp_map, ← G.map_comp, ← f.w])
 #align category_theory.costructured_arrow.post CategoryTheory.CostructuredArrow.post
 
 instance (F : B ⥤ C) (G : C ⥤ D) (S : C) : Faithful (post F G S) where

chore: fix porting note about Comma.eqToHom_right by adding simp lemmas (#7884)

There are two things going on here: the change in behaviour in simp (currently, but not for much longer, requiring zeta := false), and some defeq abuse that I'm resolving here by adding additional simp lemmas.

This will slightly clarify one of the changes required in #7847

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

b5128f3c

Diff

@@ -96,6 +96,7 @@ theorem comp_right {X Y Z : StructuredArrow S T} (f : X ⟶ Y) (g : Y ⟶ Z) :
 @[simp]
 theorem id_right (X : StructuredArrow S T) : (𝟙 X : X ⟶ X).right = 𝟙 X.right := rfl
 
+@[simp]
 theorem eqToHom_right {X Y : StructuredArrow S T} (h : X = Y) :
     (eqToHom h).right = eqToHom (by rw [h]) := by
   subst h
@@ -427,6 +428,7 @@ theorem comp_left {X Y Z : CostructuredArrow S T} (f : X ⟶ Y) (g : Y ⟶ Z) :
 @[simp]
 theorem id_left (X : CostructuredArrow S T) : (𝟙 X : X ⟶ X).left = 𝟙 X.left := rfl
 
+@[simp]
 theorem eqToHom_left {X Y : CostructuredArrow S T} (h : X = Y) :
     (eqToHom h).left = eqToHom (by rw [h]) := by
   subst h

chore: cleanup some spaces (#7484)

Purely cosmetic PR.

c93575a3

Diff

@@ -832,12 +832,12 @@ def structuredArrowOpEquivalence (F : C ⥤ D) (d : D) :
       (fun X => (StructuredArrow.isoMk (Iso.refl _)).op)
       fun {X Y} f => Quiver.Hom.unop_inj <| by
         apply CommaMorphism.ext <;>
-          dsimp [StructuredArrow.isoMk, Comma.isoMk,StructuredArrow.homMk]; simp )
+          dsimp [StructuredArrow.isoMk, Comma.isoMk,StructuredArrow.homMk]; simp)
     (NatIso.ofComponents
       (fun X => CostructuredArrow.isoMk (Iso.refl _))
       fun {X Y} f => by
         apply CommaMorphism.ext <;>
-          dsimp [CostructuredArrow.isoMk, Comma.isoMk, CostructuredArrow.homMk]; simp )
+          dsimp [CostructuredArrow.isoMk, Comma.isoMk, CostructuredArrow.homMk]; simp)
 #align category_theory.structured_arrow_op_equivalence CategoryTheory.structuredArrowOpEquivalence
 
 /-- For a functor `F : C ⥤ D` and an object `d : D`, the category of costructured arrows
@@ -852,12 +852,12 @@ def costructuredArrowOpEquivalence (F : C ⥤ D) (d : D) :
       (fun X => (CostructuredArrow.isoMk (Iso.refl _)).op)
       fun {X Y} f => Quiver.Hom.unop_inj <| by
         apply CommaMorphism.ext <;>
-          dsimp [CostructuredArrow.isoMk, CostructuredArrow.homMk, Comma.isoMk]; simp )
+          dsimp [CostructuredArrow.isoMk, CostructuredArrow.homMk, Comma.isoMk]; simp)
     (NatIso.ofComponents
       (fun X => StructuredArrow.isoMk (Iso.refl _))
       fun {X Y} f => by
         apply CommaMorphism.ext <;>
-          dsimp [StructuredArrow.isoMk, StructuredArrow.homMk, Comma.isoMk]; simp )
+          dsimp [StructuredArrow.isoMk, StructuredArrow.homMk, Comma.isoMk]; simp)
 #align category_theory.costructured_arrow_op_equivalence CategoryTheory.costructuredArrowOpEquivalence
 
 end CategoryTheory

chore: only four spaces for subsequent lines (#7286)

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

0c7d6fa5

Diff

@@ -91,11 +91,10 @@ theorem w {A B : StructuredArrow S T} (f : A ⟶ B) : A.hom ≫ T.map f.right =
 
 @[simp]
 theorem comp_right {X Y Z : StructuredArrow S T} (f : X ⟶ Y) (g : Y ⟶ Z) :
-  (f ≫ g).right = f.right ≫ g.right := rfl
+    (f ≫ g).right = f.right ≫ g.right := rfl
 
 @[simp]
-theorem id_right (X : StructuredArrow S T) :
-  (𝟙 X : X ⟶ X).right = 𝟙 X.right := rfl
+theorem id_right (X : StructuredArrow S T) : (𝟙 X : X ⟶ X).right = 𝟙 X.right := rfl
 
 theorem eqToHom_right {X Y : StructuredArrow S T} (h : X = Y) :
     (eqToHom h).right = eqToHom (by rw [h]) := by
@@ -103,8 +102,7 @@ theorem eqToHom_right {X Y : StructuredArrow S T} (h : X = Y) :
   simp only [eqToHom_refl, id_right]
 
 @[simp]
-theorem left_eq_id {X Y : StructuredArrow S T} (f : X ⟶ Y) :
-  f.left = 𝟙 _ := rfl
+theorem left_eq_id {X Y : StructuredArrow S T} (f : X ⟶ Y) : f.left = 𝟙 _ := rfl
 
 /-- To construct a morphism of structured arrows,
 we need a morphism of the objects underlying the target,
@@ -424,11 +422,10 @@ theorem w {A B : CostructuredArrow S T} (f : A ⟶ B) : S.map f.left ≫ B.hom =
 
 @[simp]
 theorem comp_left {X Y Z : CostructuredArrow S T} (f : X ⟶ Y) (g : Y ⟶ Z) :
-  (f ≫ g).left = f.left ≫ g.left := rfl
+    (f ≫ g).left = f.left ≫ g.left := rfl
 
 @[simp]
-theorem id_left (X : CostructuredArrow S T) :
-  (𝟙 X : X ⟶ X).left = 𝟙 X.left := rfl
+theorem id_left (X : CostructuredArrow S T) : (𝟙 X : X ⟶ X).left = 𝟙 X.left := rfl
 
 theorem eqToHom_left {X Y : CostructuredArrow S T} (h : X = Y) :
     (eqToHom h).left = eqToHom (by rw [h]) := by
@@ -436,8 +433,7 @@ theorem eqToHom_left {X Y : CostructuredArrow S T} (h : X = Y) :
   simp only [eqToHom_refl, id_left]
 
 @[simp]
-theorem right_eq_id {X Y : CostructuredArrow S T} (f : X ⟶ Y) :
-  f.right = 𝟙 _ := rfl
+theorem right_eq_id {X Y : CostructuredArrow S T} (f : X ⟶ Y) : f.right = 𝟙 _ := rfl
 
 /-- To construct a morphism of costructured arrows,
 we need a morphism of the objects underlying the source,

feat: upgrade a functor to a functor to structured arrows (#6787)

af001325

Diff

@@ -692,6 +692,62 @@ end IsUniversal
 
 end CostructuredArrow
 
+namespace Functor
+
+variable {E : Type u₃} [Category.{v₃} E]
+
+/-- Given `X : D` and `F : C ⥤ D`, to upgrade a functor `G : E ⥤ C` to a functor
+    `E ⥤ StructuredArrow X F`, it suffices to provide maps `X ⟶ F.obj (G.obj Y)` for all `Y` making
+    the obvious triangles involving all `F.map (G.map g)` commute.
+
+    This is of course the same as providing a cone over `F ⋙ G` with cone point `X`, see
+    `Functor.toStructuredArrowIsoToStructuredArrow`. -/
+@[simps]
+def toStructuredArrow (G : E ⥤ C) (X : D) (F : C ⥤ D) (f : (Y : E) → X ⟶ F.obj (G.obj Y))
+    (h : ∀ {Y Z : E} (g : Y ⟶ Z), f Y ≫ F.map (G.map g) = f Z) : E ⥤ StructuredArrow X F where
+  obj Y := StructuredArrow.mk (f Y)
+  map g := StructuredArrow.homMk (G.map g) (h g)
+
+/-- Upgrading a functor `E ⥤ C` to a functor `E ⥤ StructuredArrow X F` and composing with the
+    forgetful functor `StructuredArrow X F ⥤ C` recovers the original functor. -/
+def toStructuredArrowCompProj (G : E ⥤ C) (X : D) (F : C ⥤ D) (f : (Y : E) → X ⟶ F.obj (G.obj Y))
+    (h : ∀ {Y Z : E} (g : Y ⟶ Z), f Y ≫ F.map (G.map g) = f Z) :
+    G.toStructuredArrow X F f h ⋙ StructuredArrow.proj _ _ ≅ G :=
+  Iso.refl _
+
+@[simp]
+lemma toStructuredArrow_comp_proj (G : E ⥤ C) (X : D) (F : C ⥤ D)
+    (f : (Y : E) → X ⟶ F.obj (G.obj Y)) (h : ∀ {Y Z : E} (g : Y ⟶ Z), f Y ≫ F.map (G.map g) = f Z) :
+    G.toStructuredArrow X F f h ⋙ StructuredArrow.proj _ _ = G :=
+  rfl
+
+/-- Given `F : C ⥤ D` and `X : D`, to upgrade a functor `G : E ⥤ C` to a functor
+    `E ⥤ CostructuredArrow F X`, it suffices to provide maps `F.obj (G.obj Y) ⟶ X` for all `Y`
+    making the obvious triangles involving all `F.map (G.map g)` commute.
+
+    This is of course the same as providing a cocone over `F ⋙ G` with cocone point `X`, see
+    `Functor.toCostructuredArrowIsoToCostructuredArrow`. -/
+@[simps]
+def toCostructuredArrow (G : E ⥤ C) (F : C ⥤ D) (X : D) (f : (Y : E) → F.obj (G.obj Y) ⟶ X)
+    (h : ∀ {Y Z : E} (g : Y ⟶ Z), F.map (G.map g) ≫ f Z = f Y) : E ⥤ CostructuredArrow F X where
+  obj Y := CostructuredArrow.mk (f Y)
+  map g := CostructuredArrow.homMk (G.map g) (h g)
+
+/-- Upgrading a functor `E ⥤ C` to a functor `E ⥤ CostructuredArrow F X` and composing with the
+    forgetful functor `CostructuredArrow F X ⥤ C` recovers the original functor. -/
+def toCostructuredArrowCompProj (G : E ⥤ C) (F : C ⥤ D) (X : D)
+    (f : (Y : E) → F.obj (G.obj Y) ⟶ X) (h : ∀ {Y Z : E} (g : Y ⟶ Z), F.map (G.map g) ≫ f Z = f Y) :
+    G.toCostructuredArrow F X f h ⋙ CostructuredArrow.proj _ _ ≅ G :=
+  Iso.refl _
+
+@[simp]
+lemma toCostructuredArrow_comp_proj (G : E ⥤ C) (F : C ⥤ D) (X : D)
+    (f : (Y : E) → F.obj (G.obj Y) ⟶ X) (h : ∀ {Y Z : E} (g : Y ⟶ Z), F.map (G.map g) ≫ f Z = f Y) :
+    G.toCostructuredArrow F X f h ⋙ CostructuredArrow.proj _ _ = G :=
+rfl
+
+end Functor
+
 open Opposite
 
 namespace StructuredArrow

refactor: move morphisms in StructuredArrow to a lower universe (#6397)

This PR changes the definition

abbrev fromPUnit (X : C) : Discrete PUnit.{v + 1} ⥤ C :=
  (Functor.const _).obj X

abbrev fromPUnit (X : C) : Discrete PUnit.{w + 1} ⥤ C :=
  (Functor.const _).obj X

and then redefines

def StructuredArrow (S : D) (T : C ⥤ D) :=
  Comma (Functor.fromPUnit S) T

def StructuredArrow (S : D) (T : C ⥤ D) :=
  Comma (Functor.fromPUnit.{0} S) T

The effect of this is that given {C : Type u₁} [Category.{v₁} C] {D : Type u₂} [Category.{v₂} D] (S : D) (T : C ⥤ D), the morphisms of StructuredArrow S T no longer live in max v₁ v₂, but in v₁, as they should. Thus, this PR is basically a better version of #6388.

My guess for why we used to have the larger universe is that back in the day, the universes for limits were much more restricted, so stating the results of Limits/Comma.lean was not possible if the morphisms of StructuredArrow live in v₁. Luckily, by now it is possible to state everything correctly, and this PR adjusts Limits/Comma.lean and Limits/Over.lean accordingly.

7499ee49

Diff

@@ -33,9 +33,11 @@ variable {C : Type u₁} [Category.{v₁} C] {D : Type u₂} [Category.{v₂} D]
 has as its objects `D`-morphisms of the form `S ⟶ T Y`, for some `Y : C`,
 and morphisms `C`-morphisms `Y ⟶ Y'` making the obvious triangle commute.
 -/
+-- We explicitly come from `PUnit.{1}` here to obtain the correct universe for morphisms of
+-- structured arrows.
 -- @[nolint has_nonempty_instance]
 def StructuredArrow (S : D) (T : C ⥤ D) :=
-  Comma (Functor.fromPUnit S) T
+  Comma (Functor.fromPUnit.{0} S) T
 #align category_theory.structured_arrow CategoryTheory.StructuredArrow
 
 -- Porting note: not found by inferInstance
@@ -173,9 +175,6 @@ instance proj_faithful : Faithful (proj S T) where
   map_injective {_ _} := ext
 #align category_theory.structured_arrow.proj_faithful CategoryTheory.StructuredArrow.proj_faithful
 
-instance : LocallySmall.{v₁} (StructuredArrow S T) where
-  hom_small _ _ := small_of_injective ext
-
 /-- The converse of this is true with additional assumptions, see `mono_iff_mono_right`. -/
 theorem mono_of_mono_right {A B : StructuredArrow S T} (f : A ⟶ B) [h : Mono f.right] : Mono f :=
   (proj S T).mono_of_mono_map h
@@ -368,9 +367,11 @@ end StructuredArrow
 has as its objects `D`-morphisms of the form `S Y ⟶ T`, for some `Y : C`,
 and morphisms `C`-morphisms `Y ⟶ Y'` making the obvious triangle commute.
 -/
+-- We explicitly come from `PUnit.{1}` here to obtain the correct universe for morphisms of
+-- costructured arrows.
 -- @[nolint has_nonempty_instance] -- Porting note: removed
 def CostructuredArrow (S : C ⥤ D) (T : D) :=
-  Comma S (Functor.fromPUnit T)
+  Comma S (Functor.fromPUnit.{0} T)
 #align category_theory.costructured_arrow CategoryTheory.CostructuredArrow
 
 instance (S : C ⥤ D) (T : D) : Category (CostructuredArrow S T) := commaCategory
@@ -502,9 +503,6 @@ theorem ext_iff {A B : CostructuredArrow S T} (f g : A ⟶ B) : f = g ↔ f.left
 instance proj_faithful : Faithful (proj S T) where map_injective {_ _} := ext
 #align category_theory.costructured_arrow.proj_faithful CategoryTheory.CostructuredArrow.proj_faithful
 
-instance : LocallySmall.{v₁} (CostructuredArrow S T) where
-  hom_small _ _ := small_of_injective ext
-
 theorem mono_of_mono_left {A B : CostructuredArrow S T} (f : A ⟶ B) [h : Mono f.left] : Mono f :=
   (proj S T).mono_of_mono_map h
 #align category_theory.costructured_arrow.mono_of_mono_left CategoryTheory.CostructuredArrow.mono_of_mono_left

feat: functoriality of StructuredArrow.homMk' (#6813)

7a05c35f

Diff

@@ -49,7 +49,7 @@ def proj (S : D) (T : C ⥤ D) : StructuredArrow S T ⥤ C :=
   Comma.snd _ _
 #align category_theory.structured_arrow.proj CategoryTheory.StructuredArrow.proj
 
-variable {S S' S'' : D} {Y Y' : C} {T T' : C ⥤ D}
+variable {S S' S'' : D} {Y Y' Y'' : C} {T T' : C ⥤ D}
 
 -- porting note: this lemma was added because `Comma.hom_ext`
 -- was not triggered automatically
@@ -95,6 +95,11 @@ theorem comp_right {X Y Z : StructuredArrow S T} (f : X ⟶ Y) (g : Y ⟶ Z) :
 theorem id_right (X : StructuredArrow S T) :
   (𝟙 X : X ⟶ X).right = 𝟙 X.right := rfl
 
+theorem eqToHom_right {X Y : StructuredArrow S T} (h : X = Y) :
+    (eqToHom h).right = eqToHom (by rw [h]) := by
+  subst h
+  simp only [eqToHom_refl, id_right]
+
 @[simp]
 theorem left_eq_id {X Y : StructuredArrow S T} (f : X ⟶ Y) :
   f.left = 𝟙 _ := rfl
@@ -125,6 +130,22 @@ def homMk' (f : StructuredArrow S T) (g : f.right ⟶ Y') : f ⟶ mk (f.hom ≫
   right := g
 #align category_theory.structured_arrow.hom_mk' CategoryTheory.StructuredArrow.homMk'
 
+lemma homMk'_id (f : StructuredArrow S T) : homMk' f (𝟙 f.right) = eqToHom (by aesop_cat) := by
+  ext
+  simp [eqToHom_right]
+
+lemma homMk'_mk_id (f : S ⟶ T.obj Y) : homMk' (mk f) (𝟙 Y) = eqToHom (by aesop_cat) :=
+  homMk'_id _
+
+lemma homMk'_comp (f : StructuredArrow S T) (g : f.right ⟶ Y') (g' : Y' ⟶ Y'') :
+    homMk' f (g ≫ g') = homMk' f g ≫ homMk' (mk (f.hom ≫ T.map g)) g' ≫ eqToHom (by simp) := by
+  ext
+  simp [eqToHom_right]
+
+lemma homMk'_mk_comp (f : S ⟶ T.obj Y) (g : Y ⟶ Y') (g' : Y' ⟶ Y'') :
+    homMk' (mk f) (g ≫ g') = homMk' (mk f) g ≫ homMk' (mk (f ≫ T.map g)) g' ≫ eqToHom (by simp) :=
+  homMk'_comp _ _ _
+
 /-- To construct an isomorphism of structured arrows,
 we need an isomorphism of the objects underlying the target,
 and to check that the triangle commutes.
@@ -362,7 +383,7 @@ def proj (S : C ⥤ D) (T : D) : CostructuredArrow S T ⥤ C :=
   Comma.fst _ _
 #align category_theory.costructured_arrow.proj CategoryTheory.CostructuredArrow.proj
 
-variable {T T' T'' : D} {Y Y' : C} {S S' : C ⥤ D}
+variable {T T' T'' : D} {Y Y' Y'' : C} {S S' : C ⥤ D}
 
 -- porting note: this lemma was added because `Comma.hom_ext`
 -- was not triggered automatically
@@ -409,7 +430,7 @@ theorem id_left (X : CostructuredArrow S T) :
   (𝟙 X : X ⟶ X).left = 𝟙 X.left := rfl
 
 theorem eqToHom_left {X Y : CostructuredArrow S T} (h : X = Y) :
-  (eqToHom h).left = eqToHom (by rw [h]) := by
+    (eqToHom h).left = eqToHom (by rw [h]) := by
   subst h
   simp only [eqToHom_refl, id_left]
 
@@ -440,6 +461,22 @@ def homMk' (f : CostructuredArrow S T) (g : Y' ⟶ f.left) : mk (S.map g ≫ f.h
   left := g
   right := eqToHom (by ext)
 
+lemma homMk'_id (f : CostructuredArrow S T) : homMk' f (𝟙 f.left) = eqToHom (by aesop_cat) := by
+  ext
+  simp [eqToHom_left]
+
+lemma homMk'_mk_id (f : S.obj Y ⟶ T) : homMk' (mk f) (𝟙 Y) = eqToHom (by aesop_cat) :=
+  homMk'_id _
+
+lemma homMk'_comp (f : CostructuredArrow S T) (g : Y' ⟶ f.left) (g' : Y'' ⟶ Y') :
+    homMk' f (g' ≫ g) = eqToHom (by simp) ≫ homMk' (mk (S.map g ≫ f.hom)) g' ≫ homMk' f g := by
+  ext
+  simp [eqToHom_left]
+
+lemma homMk'_mk_comp (f : S.obj Y ⟶ T) (g : Y' ⟶ Y) (g' : Y'' ⟶ Y') :
+    homMk' (mk f) (g' ≫ g) = eqToHom (by simp) ≫ homMk' (mk (S.map g ≫ f)) g' ≫ homMk' (mk f) g :=
+  homMk'_comp _ _ _
+
 /-- To construct an isomorphism of costructured arrows,
 we need an isomorphism of the objects underlying the source,
 and to check that the triangle commutes.

feat(CategoryTheory/Bicategory): define left Kan extensions (#6552)

The basic design follows the API for colimits in the category theory library.

The dictionary looks like: Current PR LeftExtension <-> Limits.Cocone LeftExtension.IsKan <-> Limits.IsColimit Future PR LeftExtension.HasKan <-> Limits.HasColimit lan <-> Limits.colimit

The diagrams in the docs are far from ideal, but I hope it helps for the time being. I would be very happy to have a graphical visualization by e.g. the widgets.

f8d81046

Diff

@@ -58,6 +58,10 @@ variable {S S' S'' : D} {Y Y' : C} {T T' : C ⥤ D}
 lemma hom_ext {X Y : StructuredArrow S T} (f g : X ⟶ Y) (h : f.right = g.right) : f = g :=
   CommaMorphism.ext _ _ (Subsingleton.elim _ _) h
 
+@[simp]
+theorem hom_eq_iff {X Y : StructuredArrow S T} (f g : X ⟶ Y) : f = g ↔ f.right = g.right :=
+  ⟨fun h ↦ by rw [h], hom_ext _ _⟩
+
 /-- Construct a structured arrow from a morphism. -/
 def mk (f : S ⟶ T.obj Y) : StructuredArrow S T :=
   ⟨⟨⟨⟩⟩, Y, f⟩
@@ -300,6 +304,43 @@ instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢]
   exact Set.ext fun X => ⟨fun h => ⟨⟨⟨_, h⟩, X.hom⟩, (eq_mk _).symm⟩, by aesop_cat⟩
 #align category_theory.structured_arrow.small_proj_preimage_of_locally_small CategoryTheory.StructuredArrow.small_proj_preimage_of_locallySmall
 
+/-- A structured arrow is called universal if it is initial. -/
+abbrev IsUniversal (f : StructuredArrow S T) := IsInitial f
+
+namespace IsUniversal
+
+variable {f g : StructuredArrow S T}
+
+theorem uniq (h : IsUniversal f) (η : f ⟶ g) : η = h.to g :=
+  h.hom_ext η (h.to g)
+
+/-- The family of morphisms out of a universal arrow. -/
+def desc (h : IsUniversal f) (g : StructuredArrow S T) : f.right ⟶ g.right :=
+  (h.to g).right
+
+/-- Any structured arrow factors through a universal arrow. -/
+@[reassoc (attr := simp)]
+theorem fac (h : IsUniversal f) (g : StructuredArrow S T) :
+    f.hom ≫ T.map (h.desc g) = g.hom :=
+  Category.id_comp g.hom ▸ (h.to g).w.symm
+
+theorem hom_desc (h : IsUniversal f) {c : C} (η : f.right ⟶ c) :
+    η = h.desc (mk <| f.hom ≫ T.map η) :=
+  let g := mk <| f.hom ≫ T.map η
+  congrArg CommaMorphism.right (h.hom_ext (homMk η rfl : f ⟶ g) (h.to g))
+
+/-- Two morphisms out of a universal `T`-structured arrow are equal if their image under `T` are
+equal after precomposing the universal arrow. -/
+theorem hom_ext (h : IsUniversal f) {c : C} {η η' : f.right ⟶ c}
+    (w : f.hom ≫ T.map η = f.hom ≫ T.map η') : η = η' := by
+  rw [h.hom_desc η, h.hom_desc η', w]
+
+theorem existsUnique (h : IsUniversal f) (g : StructuredArrow S T) :
+    ∃! η : f.right ⟶ g.right, f.hom ≫ T.map η = g.hom :=
+  ⟨h.desc g, h.fac g, fun f w ↦ h.hom_ext <| by simp [w]⟩
+
+end IsUniversal
+
 end StructuredArrow
 
 /-- The category of `S`-costructured arrows with target `T : D` (here `S : C ⥤ D`),
@@ -330,6 +371,10 @@ variable {T T' T'' : D} {Y Y' : C} {S S' : C ⥤ D}
 lemma hom_ext {X Y : CostructuredArrow S T} (f g : X ⟶ Y) (h : f.left = g.left) : f = g :=
   CommaMorphism.ext _ _ h (Subsingleton.elim _ _)
 
+@[simp]
+theorem hom_eq_iff {X Y : CostructuredArrow S T} (f g : X ⟶ Y) : f = g ↔ f.left = g.left :=
+  ⟨fun h ↦ by rw [h], hom_ext _ _⟩
+
 /-- Construct a costructured arrow from a morphism. -/
 def mk (f : S.obj Y ⟶ T) : CostructuredArrow S T :=
   ⟨Y, ⟨⟨⟩⟩, f⟩
@@ -573,6 +618,43 @@ instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢]
   exact Set.ext fun X => ⟨fun h => ⟨⟨⟨_, h⟩, X.hom⟩, (eq_mk _).symm⟩, by aesop_cat⟩
 #align category_theory.costructured_arrow.small_proj_preimage_of_locally_small CategoryTheory.CostructuredArrow.small_proj_preimage_of_locallySmall
 
+/-- A costructured arrow is called universal if it is terminal. -/
+abbrev IsUniversal (f : CostructuredArrow S T) := IsTerminal f
+
+namespace IsUniversal
+
+variable {f g : CostructuredArrow S T}
+
+theorem uniq (h : IsUniversal f) (η : g ⟶ f) : η = h.from g :=
+  h.hom_ext η (h.from g)
+
+/-- The family of morphisms into a universal arrow. -/
+def lift (h : IsUniversal f) (g : CostructuredArrow S T) : g.left ⟶ f.left :=
+  (h.from g).left
+
+/-- Any costructured arrow factors through a universal arrow. -/
+@[reassoc (attr := simp)]
+theorem fac (h : IsUniversal f) (g : CostructuredArrow S T) :
+    S.map (h.lift g) ≫ f.hom = g.hom :=
+  Category.comp_id g.hom ▸ (h.from g).w
+
+theorem hom_desc (h : IsUniversal f) {c : C} (η : c ⟶ f.left) :
+    η = h.lift (mk <| S.map η ≫ f.hom) :=
+  let g := mk <| S.map η ≫ f.hom
+  congrArg CommaMorphism.left (h.hom_ext (homMk η rfl : g ⟶ f) (h.from g))
+
+/-- Two morphisms into a universal `S`-costructured arrow are equal if their image under `S` are
+equal after postcomposing the universal arrow. -/
+theorem hom_ext (h : IsUniversal f) {c : C} {η η' : c ⟶ f.left}
+    (w : S.map η ≫ f.hom = S.map η' ≫ f.hom) : η = η' := by
+  rw [h.hom_desc η, h.hom_desc η', w]
+
+theorem existsUnique (h : IsUniversal f) (g : CostructuredArrow S T) :
+    ∃! η : g.left ⟶ f.left, S.map η ≫ f.hom = g.hom :=
+  ⟨h.lift g, h.fac g, fun f w ↦ h.hom_ext <| by simp [w]⟩
+
+end IsUniversal
+
 end CostructuredArrow
 
 open Opposite

feat: every presheaf on a large category is a colimit of representables (#6387)

b48610ff

Diff

@@ -113,13 +113,12 @@ def homMk {f f' : StructuredArrow S T} (g : f.right ⟶ f'.right)
 picks up on it (seems like a bug). Either way simp solves it.  -/
 attribute [-simp, nolint simpNF] homMk_left
 
-/-- Given a structured arrow `X ⟶ F(U)`, and an arrow `U ⟶ Y`, we can construct a morphism of
-structured arrow given by `(X ⟶ F(U)) ⟶ (X ⟶ F(U) ⟶ F(Y))`.
--/
-def homMk' {F : C ⥤ D} {X : D} {Y : C} (U : StructuredArrow X F) (f : U.right ⟶ Y) :
-    U ⟶ mk (U.hom ≫ F.map f) where
+/-- Given a structured arrow `X ⟶ T(Y)`, and an arrow `Y ⟶ Y'`, we can construct a morphism of
+    structured arrows given by `(X ⟶ T(Y)) ⟶ (X ⟶ T(Y) ⟶ T(Y'))`.  -/
+@[simps]
+def homMk' (f : StructuredArrow S T) (g : f.right ⟶ Y') : f ⟶ mk (f.hom ≫ T.map g) where
   left := eqToHom (by ext)
-  right := f
+  right := g
 #align category_theory.structured_arrow.hom_mk' CategoryTheory.StructuredArrow.homMk'
 
 /-- To construct an isomorphism of structured arrows,
@@ -171,11 +170,10 @@ instance epi_homMk {A B : StructuredArrow S T} (f : A.right ⟶ B.right) (w) [h
   (proj S T).epi_of_epi_map h
 #align category_theory.structured_arrow.epi_hom_mk CategoryTheory.StructuredArrow.epi_homMk
 
-/-- Eta rule for structured arrows. Prefer `StructuredArrow.eta`, since equality of objects tends
-    to cause problems. -/
-theorem eq_mk (f : StructuredArrow S T) : f = mk f.hom := by
-  cases f
-  congr
+/-- Eta rule for structured arrows. Prefer `StructuredArrow.eta` for rewriting, since equality of
+    objects tends to cause problems. -/
+theorem eq_mk (f : StructuredArrow S T) : f = mk f.hom :=
+  rfl
 #align category_theory.structured_arrow.eq_mk CategoryTheory.StructuredArrow.eq_mk
 
 /-- Eta rule for structured arrows. -/
@@ -390,6 +388,13 @@ def homMk {f f' : CostructuredArrow S T} (g : f.left ⟶ f'.left)
 picks up on it. Either way simp can prove this -/
 attribute [-simp, nolint simpNF] homMk_right_down_down
 
+/-- Given a costructured arrow `S(Y) ⟶ X`, and an arrow `Y' ⟶ Y'`, we can construct a morphism of
+    costructured arrows given by `(S(Y) ⟶ X) ⟶ (S(Y') ⟶ S(Y) ⟶ X)`. -/
+@[simps]
+def homMk' (f : CostructuredArrow S T) (g : Y' ⟶ f.left) : mk (S.map g ≫ f.hom) ⟶ f where
+  left := g
+  right := eqToHom (by ext)
+
 /-- To construct an isomorphism of costructured arrows,
 we need an isomorphism of the objects underlying the source,
 and to check that the triangle commutes.
@@ -437,11 +442,10 @@ instance epi_homMk {A B : CostructuredArrow S T} (f : A.left ⟶ B.left) (w) [h
   (proj S T).epi_of_epi_map h
 #align category_theory.costructured_arrow.epi_hom_mk CategoryTheory.CostructuredArrow.epi_homMk
 
-/-- Eta rule for costructured arrows. Prefer `CostructuredArrow.eta`, as equality of objects tends
-    to cause problems. -/
-theorem eq_mk (f : CostructuredArrow S T) : f = mk f.hom := by
-  cases f
-  congr
+/-- Eta rule for costructured arrows. Prefer `CostructuredArrow.eta` for rewriting, as equality of
+    objects tends to cause problems. -/
+theorem eq_mk (f : CostructuredArrow S T) : f = mk f.hom :=
+  rfl
 #align category_theory.costructured_arrow.eq_mk CategoryTheory.CostructuredArrow.eq_mk
 
 /-- Eta rule for costructured arrows. -/

feat: CostructuredArrow is locally small (#6388)

5df781c2

Diff

@@ -149,6 +149,9 @@ instance proj_faithful : Faithful (proj S T) where
   map_injective {_ _} := ext
 #align category_theory.structured_arrow.proj_faithful CategoryTheory.StructuredArrow.proj_faithful
 
+instance : LocallySmall.{v₁} (StructuredArrow S T) where
+  hom_small _ _ := small_of_injective ext
+
 /-- The converse of this is true with additional assumptions, see `mono_iff_mono_right`. -/
 theorem mono_of_mono_right {A B : StructuredArrow S T} (f : A ⟶ B) [h : Mono f.right] : Mono f :=
   (proj S T).mono_of_mono_map h
@@ -412,6 +415,9 @@ theorem ext_iff {A B : CostructuredArrow S T} (f g : A ⟶ B) : f = g ↔ f.left
 instance proj_faithful : Faithful (proj S T) where map_injective {_ _} := ext
 #align category_theory.costructured_arrow.proj_faithful CategoryTheory.CostructuredArrow.proj_faithful
 
+instance : LocallySmall.{v₁} (CostructuredArrow S T) where
+  hom_small _ _ := small_of_injective ext
+
 theorem mono_of_mono_left {A B : CostructuredArrow S T} (f : A ⟶ B) [h : Mono f.left] : Mono f :=
   (proj S T).mono_of_mono_map h
 #align category_theory.costructured_arrow.mono_of_mono_left CategoryTheory.CostructuredArrow.mono_of_mono_left

feat: transfer Functor.Final across natural isomorphisms (#6232)

79a62b9e

Diff

@@ -49,7 +49,7 @@ def proj (S : D) (T : C ⥤ D) : StructuredArrow S T ⥤ C :=
   Comma.snd _ _
 #align category_theory.structured_arrow.proj CategoryTheory.StructuredArrow.proj
 
-variable {S S' S'' : D} {Y Y' : C} {T : C ⥤ D}
+variable {S S' S'' : D} {Y Y' : C} {T T' : C ⥤ D}
 
 -- porting note: this lemma was added because `Comma.hom_ext`
 -- was not triggered automatically
@@ -216,6 +216,17 @@ theorem map_comp {f : S ⟶ S'} {f' : S' ⟶ S''} {h : StructuredArrow S'' T} :
   simp
 #align category_theory.structured_arrow.map_comp CategoryTheory.StructuredArrow.map_comp
 
+/-- An isomorphism `S ≅ S'` induces an equivalence `StructuredArrow S T ≌ StructuredArrow S' T`. -/
+@[simp]
+def mapIso (i : S ≅ S') : StructuredArrow S T ≌ StructuredArrow S' T :=
+  Comma.mapLeftIso _ ((Functor.const _).mapIso i)
+
+/-- A natural isomorphism `T ≅ T'` induces an equivalence
+    `StructuredArrow S T ≌ StructuredArrow S T'`.-/
+@[simp]
+def mapNatIso (i : T ≅ T') : StructuredArrow S T ≌ StructuredArrow S T' :=
+  Comma.mapRightIso _ i
+
 instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T) where
   reflects {Y Z} f t :=
     ⟨⟨StructuredArrow.homMk
@@ -309,7 +320,7 @@ def proj (S : C ⥤ D) (T : D) : CostructuredArrow S T ⥤ C :=
   Comma.fst _ _
 #align category_theory.costructured_arrow.proj CategoryTheory.CostructuredArrow.proj
 
-variable {T T' T'' : D} {Y Y' : C} {S : C ⥤ D}
+variable {T T' T'' : D} {Y Y' : C} {S S' : C ⥤ D}
 
 -- porting note: this lemma was added because `Comma.hom_ext`
 -- was not triggered automatically
@@ -468,6 +479,18 @@ theorem map_comp {f : T ⟶ T'} {f' : T' ⟶ T''} {h : CostructuredArrow S T} :
   simp
 #align category_theory.costructured_arrow.map_comp CategoryTheory.CostructuredArrow.map_comp
 
+/-- An isomorphism `T ≅ T'` induces an equivalence
+    `CostructuredArrow S T ≌ CostructuredArrow S T'`. -/
+@[simp]
+def mapIso (i : T ≅ T') : CostructuredArrow S T ≌ CostructuredArrow S T' :=
+  Comma.mapRightIso _ ((Functor.const _).mapIso i)
+
+/-- A natural isomorphism `S ≅ S'` induces an equivalence
+    `CostrucutredArrow S T ≌ CostructuredArrow S' T`. -/
+@[simp]
+def mapNatIso (i : S ≅ S') : CostructuredArrow S T ≌ CostructuredArrow S' T :=
+  Comma.mapLeftIso _ i
+
 instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T) where
   reflects {Y Z} f t :=
     ⟨⟨CostructuredArrow.homMk

feat: sufficient condition for StructuredArrow.pre to be an equivalence (#6248)

f5d12b26

Diff

@@ -244,6 +244,20 @@ def pre (S : D) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S (F ⋙ G) ⥤ St
   Comma.preRight _ F G
 #align category_theory.structured_arrow.pre CategoryTheory.StructuredArrow.pre
 
+instance (S : D) (F : B ⥤ C) (G : C ⥤ D) [Faithful F] : Faithful (pre S F G) :=
+  show Faithful (Comma.preRight _ _ _) from inferInstance
+
+instance (S : D) (F : B ⥤ C) (G : C ⥤ D) [Full F] : Full (pre S F G) :=
+  show Full (Comma.preRight _ _ _) from inferInstance
+
+instance (S : D) (F : B ⥤ C) (G : C ⥤ D) [EssSurj F] : EssSurj (pre S F G) :=
+  show EssSurj (Comma.preRight _ _ _) from inferInstance
+
+/-- If `F` is an equivalence, then so is the functor `(S, F ⋙ G) ⥤ (S, G)`. -/
+noncomputable def isEquivalencePre (S : D) (F : B ⥤ C) (G : C ⥤ D) [IsEquivalence F] :
+    IsEquivalence (pre S F G) :=
+  Comma.isEquivalencePreRight _ _ _
+
 /-- The functor `(S, F) ⥤ (G(S), F ⋙ G)`. -/
 @[simps]
 def post (S : C) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S F ⥤ StructuredArrow (G.obj S) (F ⋙ G)
@@ -482,6 +496,20 @@ def pre (F : B ⥤ C) (G : C ⥤ D) (S : D) : CostructuredArrow (F ⋙ G) S ⥤
   Comma.preLeft F G _
 #align category_theory.costructured_arrow.pre CategoryTheory.CostructuredArrow.pre
 
+instance (F : B ⥤ C) (G : C ⥤ D) (S : D) [Faithful F] : Faithful (pre F G S) :=
+  show Faithful (Comma.preLeft _ _ _) from inferInstance
+
+instance (F : B ⥤ C) (G : C ⥤ D) (S : D) [Full F] : Full (pre F G S) :=
+  show Full (Comma.preLeft _ _ _) from inferInstance
+
+instance (F : B ⥤ C) (G : C ⥤ D) (S : D) [EssSurj F] : EssSurj (pre F G S) :=
+  show EssSurj (Comma.preLeft _ _ _) from inferInstance
+
+/-- If `F` is an equivalence, then so is the functor `(F ⋙ G, S) ⥤ (G, S)`. -/
+noncomputable def isEquivalencePre (F : B ⥤ C) (G : C ⥤ D) (S : D) [IsEquivalence F] :
+    IsEquivalence (pre F G S) :=
+  Comma.isEquivalencePreLeft _ _ _
+
 /-- The functor `(F, S) ⥤ (F ⋙ G, G(S))`. -/
 @[simps]
 def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :

feat: sufficient condition for StructuredArrow.post to be an equivalence (#6218)

f285e918

Diff

@@ -252,6 +252,20 @@ def post (S : C) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S F ⥤ Structure
   map f := StructuredArrow.homMk f.right (by simp [Functor.comp_map, ←G.map_comp, ← f.w])
 #align category_theory.structured_arrow.post CategoryTheory.StructuredArrow.post
 
+instance (S : C) (F : B ⥤ C) (G : C ⥤ D) : Faithful (post S F G) where
+  map_injective {_ _} _ _ h := by simpa [ext_iff] using h
+
+instance (S : C) (F : B ⥤ C) (G : C ⥤ D) [Faithful G] : Full (post S F G) where
+  preimage {_ _} f := homMk f.right (G.map_injective (by simpa using f.w.symm))
+
+instance (S : C) (F : B ⥤ C) (G : C ⥤ D) [Full G] : EssSurj (post S F G) where
+  mem_essImage h := ⟨mk (G.preimage h.hom), ⟨isoMk (Iso.refl _) (by simp)⟩⟩
+
+/-- If `G` is fully faithful, then `post S F G : (S, F) ⥤ (G(S), F ⋙ G)` is an equivalence. -/
+noncomputable def isEquivalencePost (S : C) (F : B ⥤ C) (G : C ⥤ D) [Full G] [Faithful G] :
+    IsEquivalence (post S F G) :=
+  Equivalence.ofFullyFaithfullyEssSurj _
+
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) := by
   suffices (proj S T).obj ⁻¹' 𝒢 = Set.range fun f : ΣG : 𝒢, S ⟶ T.obj G => mk f.2 by
@@ -476,6 +490,20 @@ def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :
   map f := CostructuredArrow.homMk f.left (by simp [Functor.comp_map, ←G.map_comp, ← f.w])
 #align category_theory.costructured_arrow.post CategoryTheory.CostructuredArrow.post
 
+instance (F : B ⥤ C) (G : C ⥤ D) (S : C) : Faithful (post F G S) where
+  map_injective {_ _} _ _ h := by simpa [ext_iff] using h
+
+instance (F : B ⥤ C) (G : C ⥤ D) (S : C) [Faithful G] : Full (post F G S) where
+  preimage {_ _} f := homMk f.left (G.map_injective (by simpa using f.w))
+
+instance (F : B ⥤ C) (G : C ⥤ D) (S : C) [Full G] : EssSurj (post F G S) where
+  mem_essImage h := ⟨mk (G.preimage h.hom), ⟨isoMk (Iso.refl _) (by simp)⟩⟩
+
+/-- If `G` is fully faithful, then `post F G S : (F, S) ⥤ (F ⋙ G, G(S))` is an equivalence. -/
+noncomputable def isEquivalencePost (S : C) (F : B ⥤ C) (G : C ⥤ D) [Full G] [Faithful G] :
+    IsEquivalence (post F G S) :=
+  Equivalence.ofFullyFaithfullyEssSurj _
+
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) := by
   suffices (proj S T).obj ⁻¹' 𝒢 = Set.range fun f : ΣG : 𝒢, S.obj G ⟶ T => mk f.2 by

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.structured_arrow
-! leanprover-community/mathlib commit 8a318021995877a44630c898d0b2bc376fceef3b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.PUnit
 import Mathlib.CategoryTheory.Comma
 import Mathlib.CategoryTheory.Limits.Shapes.Terminal
 import Mathlib.CategoryTheory.EssentiallySmall
 
+#align_import category_theory.structured_arrow from "leanprover-community/mathlib"@"8a318021995877a44630c898d0b2bc376fceef3b"
+
 /-!
 # The category of "structured arrows"

chore: remove occurrences of semicolon after space (#5713)

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.

c795bd35

Diff

@@ -83,7 +83,7 @@ theorem mk_hom_eq_self (f : S ⟶ T.obj Y) : (mk f).hom = f :=
 
 @[reassoc (attr := simp)]
 theorem w {A B : StructuredArrow S T} (f : A ⟶ B) : A.hom ≫ T.map f.right = B.hom := by
-  have := f.w ; aesop_cat
+  have := f.w; aesop_cat
 #align category_theory.structured_arrow.w CategoryTheory.StructuredArrow.w
 
 @[simp]
@@ -577,12 +577,12 @@ def structuredArrowOpEquivalence (F : C ⥤ D) (d : D) :
       (fun X => (StructuredArrow.isoMk (Iso.refl _)).op)
       fun {X Y} f => Quiver.Hom.unop_inj <| by
         apply CommaMorphism.ext <;>
-          dsimp [StructuredArrow.isoMk, Comma.isoMk,StructuredArrow.homMk] ; simp )
+          dsimp [StructuredArrow.isoMk, Comma.isoMk,StructuredArrow.homMk]; simp )
     (NatIso.ofComponents
       (fun X => CostructuredArrow.isoMk (Iso.refl _))
       fun {X Y} f => by
         apply CommaMorphism.ext <;>
-          dsimp [CostructuredArrow.isoMk, Comma.isoMk, CostructuredArrow.homMk] ; simp )
+          dsimp [CostructuredArrow.isoMk, Comma.isoMk, CostructuredArrow.homMk]; simp )
 #align category_theory.structured_arrow_op_equivalence CategoryTheory.structuredArrowOpEquivalence
 
 /-- For a functor `F : C ⥤ D` and an object `d : D`, the category of costructured arrows
@@ -597,12 +597,12 @@ def costructuredArrowOpEquivalence (F : C ⥤ D) (d : D) :
       (fun X => (CostructuredArrow.isoMk (Iso.refl _)).op)
       fun {X Y} f => Quiver.Hom.unop_inj <| by
         apply CommaMorphism.ext <;>
-          dsimp [CostructuredArrow.isoMk, CostructuredArrow.homMk, Comma.isoMk] ; simp )
+          dsimp [CostructuredArrow.isoMk, CostructuredArrow.homMk, Comma.isoMk]; simp )
     (NatIso.ofComponents
       (fun X => StructuredArrow.isoMk (Iso.refl _))
       fun {X Y} f => by
         apply CommaMorphism.ext <;>
-          dsimp [StructuredArrow.isoMk, StructuredArrow.homMk, Comma.isoMk] ; simp )
+          dsimp [StructuredArrow.isoMk, StructuredArrow.homMk, Comma.isoMk]; simp )
 #align category_theory.costructured_arrow_op_equivalence CategoryTheory.costructuredArrowOpEquivalence
 
 end CategoryTheory

feat: add Aesop rules for Discrete category (#2519)

Adds a global Aesop cases rule for the Discrete category. This rule was previously added locally in several places.

ecb36a8f

Diff

@@ -229,8 +229,6 @@ instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T) where
 
 open CategoryTheory.Limits
 
-attribute [local aesop safe cases (rule_sets [CategoryTheory])] Discrete
-
 /-- The identity structured arrow is initial. -/
 def mkIdInitial [Full T] [Faithful T] : IsInitial (mk (𝟙 (T.obj Y))) where
   desc c := homMk (T.preimage c.pt.hom)
@@ -455,8 +453,6 @@ instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T) where
 
 open CategoryTheory.Limits
 
-attribute [local aesop safe cases (rule_sets [CategoryTheory])] Discrete
-
 /-- The identity costructured arrow is terminal. -/
 def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y))) where
   lift c := homMk (S.preimage c.pt.hom)

feat: more consistent use of ext, and updating porting notes. (#5242)

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

dbae2f17

Diff

@@ -56,6 +56,7 @@ variable {S S' S'' : D} {Y Y' : C} {T : C ⥤ D}
 
 -- porting note: this lemma was added because `Comma.hom_ext`
 -- was not triggered automatically
+-- See https://github.com/leanprover-community/mathlib4/issues/5229
 @[ext]
 lemma hom_ext {X Y : StructuredArrow S T} (f g : X ⟶ Y) (h : f.right = g.right) : f = g :=
   CommaMorphism.ext _ _ (Subsingleton.elim _ _) h
@@ -289,6 +290,7 @@ variable {T T' T'' : D} {Y Y' : C} {S : C ⥤ D}
 
 -- porting note: this lemma was added because `Comma.hom_ext`
 -- was not triggered automatically
+-- See https://github.com/leanprover-community/mathlib4/issues/5229
 @[ext]
 lemma hom_ext {X Y : CostructuredArrow S T} (f g : X ⟶ Y) (h : f.left = g.left) : f = g :=
   CommaMorphism.ext _ _ h (Subsingleton.elim _ _)
@@ -448,7 +450,7 @@ instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T) where
     ⟨⟨CostructuredArrow.homMk
         (inv ((proj S T).map f))
         (by rw [Functor.map_inv, IsIso.inv_comp_eq]; simp),
-      by constructor <;> apply Comma.hom_ext <;> dsimp at t ⊢ <;> simp⟩⟩
+      by constructor <;> ext <;> dsimp at t ⊢ <;> simp⟩⟩
 #align category_theory.costructured_arrow.proj_reflects_iso CategoryTheory.CostructuredArrow.proj_reflectsIsomorphisms
 
 open CategoryTheory.Limits
@@ -460,10 +462,9 @@ def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y))) where
   lift c := homMk (S.preimage c.pt.hom)
   uniq := by
     rintro c m -
-    apply CommaMorphism.ext
-    · apply S.map_injective
-      simpa only [homMk_left, S.image_preimage, ← w m] using (Category.comp_id _).symm
-    · aesop_cat
+    ext
+    apply S.map_injective
+    simpa only [homMk_left, S.image_preimage, ← w m] using (Category.comp_id _).symm
 #align category_theory.costructured_arrow.mk_id_terminal CategoryTheory.CostructuredArrow.mkIdTerminal
 
 variable {A : Type u₃} [Category.{v₃} A] {B : Type u₄} [Category.{v₄} B]

chore: formatting issues (#4947)

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

5068808d

Diff

@@ -276,6 +276,7 @@ def CostructuredArrow (S : C ⥤ D) (T : D) :=
 #align category_theory.costructured_arrow CategoryTheory.CostructuredArrow
 
 instance (S : C ⥤ D) (T : D) : Category (CostructuredArrow S T) := commaCategory
+
 namespace CostructuredArrow
 
 /-- The obvious projection functor from costructured arrows. -/

chore: review of automation in category theory (#4793)

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>

5b958613

Diff

@@ -102,8 +102,8 @@ we need a morphism of the objects underlying the target,
 and to check that the triangle commutes.
 -/
 @[simps]
-def homMk {f f' : StructuredArrow S T} (g : f.right ⟶ f'.right) (w : f.hom ≫ T.map g = f'.hom) :
-    f ⟶ f' where
+def homMk {f f' : StructuredArrow S T} (g : f.right ⟶ f'.right)
+    (w : f.hom ≫ T.map g = f'.hom := by aesop_cat) : f ⟶ f' where
   left := eqToHom (by ext)
   right := g
   w := by
@@ -129,7 +129,8 @@ we need an isomorphism of the objects underlying the target,
 and to check that the triangle commutes.
 -/
 @[simps!]
-def isoMk {f f' : StructuredArrow S T} (g : f.right ≅ f'.right) (w : f.hom ≫ T.map g.hom = f'.hom) :
+def isoMk {f f' : StructuredArrow S T} (g : f.right ≅ f'.right)
+    (w : f.hom ≫ T.map g.hom = f'.hom := by aesop_cat) :
     f ≅ f' :=
   Comma.isoMk (eqToIso (by ext)) g (by simpa [eqToHom_map] using w.symm)
 #align category_theory.structured_arrow.iso_mk CategoryTheory.StructuredArrow.isoMk
@@ -179,7 +180,7 @@ theorem eq_mk (f : StructuredArrow S T) : f = mk f.hom := by
 /-- Eta rule for structured arrows. -/
 @[simps!]
 def eta (f : StructuredArrow S T) : f ≅ mk f.hom :=
-  isoMk (Iso.refl _) (by aesop_cat)
+  isoMk (Iso.refl _)
 #align category_theory.structured_arrow.eta CategoryTheory.StructuredArrow.eta
 
 /- Porting note : it appears the simp lemma is not getting generated but the linter
@@ -231,7 +232,7 @@ attribute [local aesop safe cases (rule_sets [CategoryTheory])] Discrete
 
 /-- The identity structured arrow is initial. -/
 def mkIdInitial [Full T] [Faithful T] : IsInitial (mk (𝟙 (T.obj Y))) where
-  desc c := homMk (T.preimage c.pt.hom) (by simp)
+  desc c := homMk (T.preimage c.pt.hom)
   uniq c m _ := by
     apply CommaMorphism.ext
     · aesop_cat
@@ -338,8 +339,8 @@ we need a morphism of the objects underlying the source,
 and to check that the triangle commutes.
 -/
 @[simps!]
-def homMk {f f' : CostructuredArrow S T} (g : f.left ⟶ f'.left) (w : S.map g ≫ f'.hom = f.hom) :
-    f ⟶ f' where
+def homMk {f f' : CostructuredArrow S T} (g : f.left ⟶ f'.left)
+    (w : S.map g ≫ f'.hom = f.hom := by aesop_cat) : f ⟶ f' where
   left := g
   right := eqToHom (by ext)
   w := by simpa [eqToHom_map] using w
@@ -354,8 +355,8 @@ we need an isomorphism of the objects underlying the source,
 and to check that the triangle commutes.
 -/
 @[simps!]
-def isoMk {f f' : CostructuredArrow S T} (g : f.left ≅ f'.left) (w : S.map g.hom ≫ f'.hom = f.hom) :
-    f ≅ f' :=
+def isoMk {f f' : CostructuredArrow S T} (g : f.left ≅ f'.left)
+    (w : S.map g.hom ≫ f'.hom = f.hom := by aesop_cat) : f ≅ f' :=
   Comma.isoMk g (eqToIso (by ext)) (by simpa [eqToHom_map] using w)
 #align category_theory.costructured_arrow.iso_mk CategoryTheory.CostructuredArrow.isoMk
 
@@ -403,7 +404,7 @@ theorem eq_mk (f : CostructuredArrow S T) : f = mk f.hom := by
 /-- Eta rule for costructured arrows. -/
 @[simps!]
 def eta (f : CostructuredArrow S T) : f ≅ mk f.hom :=
-  isoMk (Iso.refl _) (by aesop_cat)
+  isoMk (Iso.refl _)
 #align category_theory.costructured_arrow.eta CategoryTheory.CostructuredArrow.eta
 
 /- Porting note : it appears the simp lemma is not getting generated but the linter
@@ -455,7 +456,7 @@ attribute [local aesop safe cases (rule_sets [CategoryTheory])] Discrete
 
 /-- The identity costructured arrow is terminal. -/
 def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y))) where
-  lift c := homMk (S.preimage c.pt.hom) (by simp)
+  lift c := homMk (S.preimage c.pt.hom)
   uniq := by
     rintro c m -
     apply CommaMorphism.ext
@@ -575,18 +576,15 @@ def structuredArrowOpEquivalence (F : C ⥤ D) (d : D) :
   Equivalence.mk (StructuredArrow.toCostructuredArrow F d)
     (CostructuredArrow.toStructuredArrow' F d).rightOp
     (NatIso.ofComponents
-      (fun X =>
-        (@StructuredArrow.isoMk _ _ _ _ _ _ (StructuredArrow.mk (unop X).hom) (unop X) (Iso.refl _)
-            (by aesop_cat)).op)
+      (fun X => (StructuredArrow.isoMk (Iso.refl _)).op)
       fun {X Y} f => Quiver.Hom.unop_inj <| by
         apply CommaMorphism.ext <;>
-          dsimp [StructuredArrow.isoMk,Comma.isoMk,StructuredArrow.homMk] ; simp )
+          dsimp [StructuredArrow.isoMk, Comma.isoMk,StructuredArrow.homMk] ; simp )
     (NatIso.ofComponents
-      (fun X =>
-        @CostructuredArrow.isoMk _ _ _ _ _ _ (CostructuredArrow.mk X.hom) X (Iso.refl _)
-          (by aesop_cat)) fun {X Y} f => by
-            apply CommaMorphism.ext <;>
-              dsimp [CostructuredArrow.isoMk, Comma.isoMk, CostructuredArrow.homMk] ; simp )
+      (fun X => CostructuredArrow.isoMk (Iso.refl _))
+      fun {X Y} f => by
+        apply CommaMorphism.ext <;>
+          dsimp [CostructuredArrow.isoMk, Comma.isoMk, CostructuredArrow.homMk] ; simp )
 #align category_theory.structured_arrow_op_equivalence CategoryTheory.structuredArrowOpEquivalence
 
 /-- For a functor `F : C ⥤ D` and an object `d : D`, the category of costructured arrows
@@ -598,18 +596,15 @@ def costructuredArrowOpEquivalence (F : C ⥤ D) (d : D) :
   Equivalence.mk (CostructuredArrow.toStructuredArrow F d)
     (StructuredArrow.toCostructuredArrow' F d).rightOp
     (NatIso.ofComponents
-      (fun X =>
-        (@CostructuredArrow.isoMk _ _ _ _ _ _ (CostructuredArrow.mk (unop X).hom) (unop X)
-            (Iso.refl _) (by aesop_cat)).op)
+      (fun X => (CostructuredArrow.isoMk (Iso.refl _)).op)
       fun {X Y} f => Quiver.Hom.unop_inj <| by
         apply CommaMorphism.ext <;>
           dsimp [CostructuredArrow.isoMk, CostructuredArrow.homMk, Comma.isoMk] ; simp )
     (NatIso.ofComponents
-      (fun X =>
-        @StructuredArrow.isoMk _ _ _ _ _ _ (StructuredArrow.mk X.hom) X (Iso.refl _)
-          (by aesop_cat)) fun {X Y} f => by
-            apply CommaMorphism.ext <;>
-              dsimp [StructuredArrow.isoMk, StructuredArrow.homMk, Comma.isoMk] ; simp )
+      (fun X => StructuredArrow.isoMk (Iso.refl _))
+      fun {X Y} f => by
+        apply CommaMorphism.ext <;>
+          dsimp [StructuredArrow.isoMk, StructuredArrow.homMk, Comma.isoMk] ; simp )
 #align category_theory.costructured_arrow_op_equivalence CategoryTheory.costructuredArrowOpEquivalence
 
 end CategoryTheory

chore: cleanup Discrete porting notes (#4780)

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

86ade6e9

Diff

@@ -227,12 +227,11 @@ instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T) where
 
 open CategoryTheory.Limits
 
--- attribute [local tidy] tactic.discrete_cases
+attribute [local aesop safe cases (rule_sets [CategoryTheory])] Discrete
 
 /-- The identity structured arrow is initial. -/
 def mkIdInitial [Full T] [Faithful T] : IsInitial (mk (𝟙 (T.obj Y))) where
   desc c := homMk (T.preimage c.pt.hom) (by simp)
-  fac := fun _ ⟨a⟩ => by cases a
   uniq c m _ := by
     apply CommaMorphism.ext
     · aesop_cat
@@ -452,12 +451,11 @@ instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T) where
 
 open CategoryTheory.Limits
 
--- attribute [local tidy] tactic.discrete_cases -- Porting note: removed
+attribute [local aesop safe cases (rule_sets [CategoryTheory])] Discrete
 
 /-- The identity costructured arrow is terminal. -/
 def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y))) where
   lift c := homMk (S.preimage c.pt.hom) (by simp)
-  fac := fun _ ⟨a⟩ => by cases a
   uniq := by
     rintro c m -
     apply CommaMorphism.ext

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

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

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

14167e48

Diff

@@ -484,8 +484,7 @@ def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :
 
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) := by
-  suffices (proj S T).obj ⁻¹' 𝒢 = Set.range fun f : ΣG : 𝒢, S.obj G ⟶ T => mk f.2
-    by
+  suffices (proj S T).obj ⁻¹' 𝒢 = Set.range fun f : ΣG : 𝒢, S.obj G ⟶ T => mk f.2 by
     rw [this]
     infer_instance
   exact Set.ext fun X => ⟨fun h => ⟨⟨⟨_, h⟩, X.hom⟩, (eq_mk _).symm⟩, by aesop_cat⟩

chore: forward port #18440 (#3183)

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

2cea862f

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz, Scott Morrison
 
 ! This file was ported from Lean 3 source module category_theory.structured_arrow
-! leanprover-community/mathlib commit fef8efdf78f223294c34a41875923ab1272322d4
+! leanprover-community/mathlib commit 8a318021995877a44630c898d0b2bc376fceef3b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -120,7 +120,7 @@ structured arrow given by `(X ⟶ F(U)) ⟶ (X ⟶ F(U) ⟶ F(Y))`.
 -/
 def homMk' {F : C ⥤ D} {X : D} {Y : C} (U : StructuredArrow X F) (f : U.right ⟶ Y) :
     U ⟶ mk (U.hom ≫ F.map f) where
-  left := by cases U.left; exact 𝟙 _
+  left := eqToHom (by ext)
   right := f
 #align category_theory.structured_arrow.hom_mk' CategoryTheory.StructuredArrow.homMk'
 
@@ -252,14 +252,8 @@ def pre (S : D) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S (F ⋙ G) ⥤ St
 @[simps]
 def post (S : C) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S F ⥤ StructuredArrow (G.obj S) (F ⋙ G)
     where
-  obj X :=
-    { left := ⟨⟨⟩⟩
-      right := X.right
-      hom := G.map X.hom }
-  map f :=
-    { left := 𝟙 ⟨⟨⟩⟩
-      right := f.right
-      w := by simp [Functor.comp_map, ← G.map_comp, ← f.w] }
+  obj X := StructuredArrow.mk (G.map X.hom)
+  map f := StructuredArrow.homMk f.right (by simp [Functor.comp_map, ←G.map_comp, ← f.w])
 #align category_theory.structured_arrow.post CategoryTheory.StructuredArrow.post
 
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
@@ -484,14 +478,8 @@ def pre (F : B ⥤ C) (G : C ⥤ D) (S : D) : CostructuredArrow (F ⋙ G) S ⥤
 @[simps]
 def post (F : B ⥤ C) (G : C ⥤ D) (S : C) :
     CostructuredArrow F S ⥤ CostructuredArrow (F ⋙ G) (G.obj S) where
-  obj X :=
-    { left := X.left
-      right := ⟨⟨⟩⟩
-      hom := G.map X.hom }
-  map f :=
-    { left := f.left
-      right := 𝟙 _
-      w := by simp [Functor.comp_map, ← G.map_comp, ← f.w] }
+  obj X := CostructuredArrow.mk (G.map X.hom)
+  map f := CostructuredArrow.homMk f.left (by simp [Functor.comp_map, ←G.map_comp, ← f.w])
 #align category_theory.costructured_arrow.post CategoryTheory.CostructuredArrow.post
 
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :

feat: port CategoryTheory.Elements (#2815)

Co-authored-by: Calvin Lee <calvins.lee@utah.edu> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>

de2321d0

Diff

@@ -54,6 +54,12 @@ def proj (S : D) (T : C ⥤ D) : StructuredArrow S T ⥤ C :=
 
 variable {S S' S'' : D} {Y Y' : C} {T : C ⥤ D}
 
+-- porting note: this lemma was added because `Comma.hom_ext`
+-- was not triggered automatically
+@[ext]
+lemma hom_ext {X Y : StructuredArrow S T} (f g : X ⟶ Y) (h : f.right = g.right) : f = g :=
+  CommaMorphism.ext _ _ (Subsingleton.elim _ _) h
+
 /-- Construct a structured arrow from a morphism. -/
 def mk (f : S ⟶ T.obj Y) : StructuredArrow S T :=
   ⟨⟨⟨⟩⟩, Y, f⟩
@@ -286,6 +292,12 @@ def proj (S : C ⥤ D) (T : D) : CostructuredArrow S T ⥤ C :=
 
 variable {T T' T'' : D} {Y Y' : C} {S : C ⥤ D}
 
+-- porting note: this lemma was added because `Comma.hom_ext`
+-- was not triggered automatically
+@[ext]
+lemma hom_ext {X Y : CostructuredArrow S T} (f g : X ⟶ Y) (h : f.left = g.left) : f = g :=
+  CommaMorphism.ext _ _ h (Subsingleton.elim _ _)
+
 /-- Construct a costructured arrow from a morphism. -/
 def mk (f : S.obj Y ⟶ T) : CostructuredArrow S T :=
   ⟨Y, ⟨⟨⟩⟩, f⟩
@@ -319,6 +331,11 @@ theorem comp_left {X Y Z : CostructuredArrow S T} (f : X ⟶ Y) (g : Y ⟶ Z) :
 theorem id_left (X : CostructuredArrow S T) :
   (𝟙 X : X ⟶ X).left = 𝟙 X.left := rfl
 
+theorem eqToHom_left {X Y : CostructuredArrow S T} (h : X = Y) :
+  (eqToHom h).left = eqToHom (by rw [h]) := by
+  subst h
+  simp only [eqToHom_refl, id_left]
+
 @[simp]
 theorem right_eq_id {X Y : CostructuredArrow S T} (f : X ⟶ Y) :
   f.right = 𝟙 _ := rfl

chore: tidy various files (#2742)

8c7b65ad

Diff

@@ -105,8 +105,8 @@ def homMk {f f' : StructuredArrow S T} (g : f.right ⟶ f'.right) (w : f.hom ≫
     simpa using w.symm
 #align category_theory.structured_arrow.hom_mk CategoryTheory.StructuredArrow.homMk
 
-/- Porting note : it appears the simp lemma is not getting generated but the linter 
-picks up on it (seems like a bug). Either way simp solves it.  -/ 
+/- Porting note : it appears the simp lemma is not getting generated but the linter
+picks up on it (seems like a bug). Either way simp solves it.  -/
 attribute [-simp, nolint simpNF] homMk_left
 
 /-- Given a structured arrow `X ⟶ F(U)`, and an arrow `U ⟶ Y`, we can construct a morphism of
@@ -128,12 +128,11 @@ def isoMk {f f' : StructuredArrow S T} (g : f.right ≅ f'.right) (w : f.hom ≫
   Comma.isoMk (eqToIso (by ext)) g (by simpa [eqToHom_map] using w.symm)
 #align category_theory.structured_arrow.iso_mk CategoryTheory.StructuredArrow.isoMk
 
-/- Porting note : it appears the simp lemma is not getting generated but the linter 
-picks up on it. Either way simp solves these. -/ 
+/- Porting note : it appears the simp lemma is not getting generated but the linter
+picks up on it. Either way simp solves these. -/
 attribute [-simp, nolint simpNF] isoMk_hom_left_down_down isoMk_inv_left_down_down
 
 theorem ext {A B : StructuredArrow S T} (f g : A ⟶ B) : f.right = g.right → f = g :=
-  --have : Subsingleton (A.left ⟶  B.left) := sorry
   CommaMorphism.ext _ _ (Subsingleton.elim _ _)
 #align category_theory.structured_arrow.ext CategoryTheory.StructuredArrow.ext
 
@@ -164,7 +163,7 @@ instance epi_homMk {A B : StructuredArrow S T} (f : A.right ⟶ B.right) (w) [h
   (proj S T).epi_of_epi_map h
 #align category_theory.structured_arrow.epi_hom_mk CategoryTheory.StructuredArrow.epi_homMk
 
-/-- Eta rule for structured arrows. Prefer `structured_arrow.eta`, since equality of objects tends
+/-- Eta rule for structured arrows. Prefer `StructuredArrow.eta`, since equality of objects tends
     to cause problems. -/
 theorem eq_mk (f : StructuredArrow S T) : f = mk f.hom := by
   cases f
@@ -177,13 +176,13 @@ def eta (f : StructuredArrow S T) : f ≅ mk f.hom :=
   isoMk (Iso.refl _) (by aesop_cat)
 #align category_theory.structured_arrow.eta CategoryTheory.StructuredArrow.eta
 
-/- Porting note : it appears the simp lemma is not getting generated but the linter 
-picks up on it. Either way simp solves these. -/ 
+/- Porting note : it appears the simp lemma is not getting generated but the linter
+picks up on it. Either way simp solves these. -/
 attribute [-simp, nolint simpNF] eta_hom_left_down_down eta_inv_left_down_down
 
 /-- A morphism between source objects `S ⟶ S'`
 contravariantly induces a functor between structured arrows,
-`structured_arrow S' T ⥤ structured_arrow S T`.
+`StructuredArrow S' T ⥤ StructuredArrow S T`.
 
 Ideally this would be described as a 2-functor from `D`
 (promoted to a 2-category with equations as 2-morphisms)
@@ -212,15 +211,13 @@ theorem map_comp {f : S ⟶ S'} {f' : S' ⟶ S''} {h : StructuredArrow S'' T} :
   simp
 #align category_theory.structured_arrow.map_comp CategoryTheory.StructuredArrow.map_comp
 
-instance proj_reflects_iso : ReflectsIsomorphisms (proj S T) where
+instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T) where
   reflects {Y Z} f t :=
-    ⟨⟨StructuredArrow.homMk (inv ((proj S T).map f))
-    (by rw [Functor.map_inv, IsIso.comp_inv_eq] ; simp), by
-      --split <-- fails!?
-      refine ⟨?_,?_⟩ -- works
-      · apply CommaMorphism.ext <;> dsimp at t ⊢ ; simp
-      · apply CommaMorphism.ext <;> dsimp at t ⊢ ; simp ⟩⟩
-#align category_theory.structured_arrow.proj_reflects_iso CategoryTheory.StructuredArrow.proj_reflects_iso
+    ⟨⟨StructuredArrow.homMk
+        (inv ((proj S T).map f))
+        (by rw [Functor.map_inv, IsIso.comp_inv_eq]; simp),
+      by constructor <;> apply CommaMorphism.ext <;> dsimp at t ⊢ <;> simp⟩⟩
+#align category_theory.structured_arrow.proj_reflects_iso CategoryTheory.StructuredArrow.proj_reflectsIsomorphisms
 
 open CategoryTheory.Limits
 
@@ -228,11 +225,7 @@ open CategoryTheory.Limits
 
 /-- The identity structured arrow is initial. -/
 def mkIdInitial [Full T] [Faithful T] : IsInitial (mk (𝟙 (T.obj Y))) where
-  desc c :=
-    homMk (T.preimage c.pt.hom)
-      (by
-        dsimp
-        simp)
+  desc c := homMk (T.preimage c.pt.hom) (by simp)
   fac := fun _ ⟨a⟩ => by cases a
   uniq c m _ := by
     apply CommaMorphism.ext
@@ -265,8 +258,7 @@ def post (S : C) (F : B ⥤ C) (G : C ⥤ D) : StructuredArrow S F ⥤ Structure
 
 instance small_proj_preimage_of_locallySmall {𝒢 : Set C} [Small.{v₁} 𝒢] [LocallySmall.{v₁} D] :
     Small.{v₁} ((proj S T).obj ⁻¹' 𝒢) := by
-  suffices (proj S T).obj ⁻¹' 𝒢 = Set.range fun f : ΣG : 𝒢, S ⟶ T.obj G => mk f.2
-    by
+  suffices (proj S T).obj ⁻¹' 𝒢 = Set.range fun f : ΣG : 𝒢, S ⟶ T.obj G => mk f.2 by
     rw [this]
     infer_instance
   exact Set.ext fun X => ⟨fun h => ⟨⟨⟨_, h⟩, X.hom⟩, (eq_mk _).symm⟩, by aesop_cat⟩
@@ -343,8 +335,8 @@ def homMk {f f' : CostructuredArrow S T} (g : f.left ⟶ f'.left) (w : S.map g 
   w := by simpa [eqToHom_map] using w
 #align category_theory.costructured_arrow.hom_mk CategoryTheory.CostructuredArrow.homMk
 
-/- Porting note : it appears the simp lemma is not getting generated but the linter 
-picks up on it. Either way simp can prove this -/ 
+/- Porting note : it appears the simp lemma is not getting generated but the linter
+picks up on it. Either way simp can prove this -/
 attribute [-simp, nolint simpNF] homMk_right_down_down
 
 /-- To construct an isomorphism of costructured arrows,
@@ -357,8 +349,8 @@ def isoMk {f f' : CostructuredArrow S T} (g : f.left ≅ f'.left) (w : S.map g.h
   Comma.isoMk g (eqToIso (by ext)) (by simpa [eqToHom_map] using w)
 #align category_theory.costructured_arrow.iso_mk CategoryTheory.CostructuredArrow.isoMk
 
-/- Porting note : it appears the simp lemma is not getting generated but the linter 
-picks up on it. Either way simp solves these. -/ 
+/- Porting note : it appears the simp lemma is not getting generated but the linter
+picks up on it. Either way simp solves these. -/
 attribute [-simp, nolint simpNF] isoMk_hom_right_down_down isoMk_inv_right_down_down
 
 theorem ext {A B : CostructuredArrow S T} (f g : A ⟶ B) (h : f.left = g.left) : f = g :=
@@ -391,7 +383,7 @@ instance epi_homMk {A B : CostructuredArrow S T} (f : A.left ⟶ B.left) (w) [h
   (proj S T).epi_of_epi_map h
 #align category_theory.costructured_arrow.epi_hom_mk CategoryTheory.CostructuredArrow.epi_homMk
 
-/-- Eta rule for costructured arrows. Prefer `costructured_arrow.eta`, as equality of objects tends
+/-- Eta rule for costructured arrows. Prefer `CostructuredArrow.eta`, as equality of objects tends
     to cause problems. -/
 theorem eq_mk (f : CostructuredArrow S T) : f = mk f.hom := by
   cases f
@@ -404,13 +396,13 @@ def eta (f : CostructuredArrow S T) : f ≅ mk f.hom :=
   isoMk (Iso.refl _) (by aesop_cat)
 #align category_theory.costructured_arrow.eta CategoryTheory.CostructuredArrow.eta
 
-/- Porting note : it appears the simp lemma is not getting generated but the linter 
-picks up on it. Either way simp solves these. -/ 
+/- Porting note : it appears the simp lemma is not getting generated but the linter
+picks up on it. Either way simp solves these. -/
 attribute [-simp, nolint simpNF] eta_hom_right_down_down eta_inv_right_down_down
 
 /-- A morphism between target objects `T ⟶ T'`
 covariantly induces a functor between costructured arrows,
-`costructured_arrow S T ⥤ costructured_arrow S T'`.
+`CostructuredArrow S T ⥤ CostructuredArrow S T'`.
 
 Ideally this would be described as a 2-functor from `D`
 (promoted to a 2-category with equations as 2-morphisms)
@@ -439,14 +431,13 @@ theorem map_comp {f : T ⟶ T'} {f' : T' ⟶ T''} {h : CostructuredArrow S T} :
   simp
 #align category_theory.costructured_arrow.map_comp CategoryTheory.CostructuredArrow.map_comp
 
-instance proj_reflects_iso : ReflectsIsomorphisms (proj S T) where
+instance proj_reflectsIsomorphisms : ReflectsIsomorphisms (proj S T) where
   reflects {Y Z} f t :=
-    ⟨⟨CostructuredArrow.homMk (inv ((proj S T).map f))
-    (by rw [Functor.map_inv, IsIso.inv_comp_eq] ; simp), by
-      refine ⟨?_,?_⟩
-      · apply Comma.hom_ext <;> dsimp at t ⊢ ; simp
-      · apply Comma.hom_ext <;> dsimp at t ⊢ ; simp ⟩⟩
-#align category_theory.costructured_arrow.proj_reflects_iso CategoryTheory.CostructuredArrow.proj_reflects_iso
+    ⟨⟨CostructuredArrow.homMk
+        (inv ((proj S T).map f))
+        (by rw [Functor.map_inv, IsIso.inv_comp_eq]; simp),
+      by constructor <;> apply Comma.hom_ext <;> dsimp at t ⊢ <;> simp⟩⟩
+#align category_theory.costructured_arrow.proj_reflects_iso CategoryTheory.CostructuredArrow.proj_reflectsIsomorphisms
 
 open CategoryTheory.Limits
 
@@ -454,11 +445,7 @@ open CategoryTheory.Limits
 
 /-- The identity costructured arrow is terminal. -/
 def mkIdTerminal [Full S] [Faithful S] : IsTerminal (mk (𝟙 (S.obj Y))) where
-  lift c :=
-    homMk (S.preimage c.pt.hom)
-      (by
-        dsimp
-        simp)
+  lift c := homMk (S.preimage c.pt.hom) (by simp)
   fac := fun _ ⟨a⟩ => by cases a
   uniq := by
     rintro c m -
@@ -624,4 +611,3 @@ def costructuredArrowOpEquivalence (F : C ⥤ D) (d : D) :
 #align category_theory.costructured_arrow_op_equivalence CategoryTheory.costructuredArrowOpEquivalence
 
 end CategoryTheory
-