category_theory.bicategory.functor
⟷
Mathlib.CategoryTheory.Bicategory.Functor
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
-import Mathbin.CategoryTheory.Bicategory.Basic
+import CategoryTheory.Bicategory.Basic
#align_import category_theory.bicategory.functor from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d
@@ -208,20 +208,6 @@ structure OplaxFunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u
namespace OplaxFunctor
-restate_axiom map_comp_naturality_left'
-
-restate_axiom map_comp_naturality_right'
-
-restate_axiom map₂_id'
-
-restate_axiom map₂_comp'
-
-restate_axiom map₂_associator'
-
-restate_axiom map₂_left_unitor'
-
-restate_axiom map₂_right_unitor'
-
attribute [simp] map_comp_naturality_left map_comp_naturality_right map₂_id map₂_associator
attribute [reassoc] map_comp_naturality_left map_comp_naturality_right map₂_comp map₂_associator
@@ -336,10 +322,6 @@ structure PseudoCore (F : OplaxFunctor B C) where
#align category_theory.oplax_functor.pseudo_core CategoryTheory.OplaxFunctor.PseudoCore
-/
-restate_axiom pseudo_core.map_id_iso_hom'
-
-restate_axiom pseudo_core.map_comp_iso_hom'
-
attribute [simp] pseudo_core.map_id_iso_hom pseudo_core.map_comp_iso_hom
end
@@ -410,20 +392,6 @@ structure Pseudofunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u
namespace Pseudofunctor
-restate_axiom map₂_id'
-
-restate_axiom map₂_comp'
-
-restate_axiom map₂_whisker_left'
-
-restate_axiom map₂_whisker_right'
-
-restate_axiom map₂_associator'
-
-restate_axiom map₂_left_unitor'
-
-restate_axiom map₂_right_unitor'
-
attribute [reassoc] map₂_comp map₂_whisker_left map₂_whisker_right map₂_associator map₂_left_unitor
map₂_right_unitor
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-
-! This file was ported from Lean 3 source module category_theory.bicategory.functor
-! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Bicategory.Basic
+#align_import category_theory.bicategory.functor from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
+
/-!
# Oplax functors and pseudofunctors
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -265,6 +265,7 @@ theorem to_prelaxFunctor_map₂ : @PrelaxFunctor.map₂ B _ _ C _ _ F = @map₂
rfl
#align category_theory.oplax_functor.to_prelax_functor_map₂ CategoryTheory.OplaxFunctor.to_prelaxFunctor_map₂
+#print CategoryTheory.OplaxFunctor.mapFunctor /-
/-- Function between 1-morphisms as a functor. -/
@[simps]
def mapFunctor (a b : B) : (a ⟶ b) ⥤ (F.obj a ⟶ F.obj b)
@@ -272,6 +273,7 @@ def mapFunctor (a b : B) : (a ⟶ b) ⥤ (F.obj a ⟶ F.obj b)
obj f := F.map f
map f g η := F.zipWith η
#align category_theory.oplax_functor.map_functor CategoryTheory.OplaxFunctor.mapFunctor
+-/
#print CategoryTheory.OplaxFunctor.id /-
/-- The identity oplax functor. -/
@@ -486,10 +488,12 @@ theorem toOplax_eq_coe : F.toOplax = F :=
rfl
#align category_theory.pseudofunctor.to_oplax_eq_coe CategoryTheory.Pseudofunctor.toOplax_eq_coe
+#print CategoryTheory.Pseudofunctor.to_oplax_obj /-
@[simp]
theorem to_oplax_obj : (F : OplaxFunctor B C).obj = F.obj :=
rfl
#align category_theory.pseudofunctor.to_oplax_obj CategoryTheory.Pseudofunctor.to_oplax_obj
+-/
@[simp]
theorem to_oplax_map : @OplaxFunctor.map B _ C _ F = @map _ _ _ _ F :=
@@ -501,22 +505,28 @@ theorem to_oplax_map₂ : @OplaxFunctor.map₂ B _ C _ F = @map₂ _ _ _ _ F :=
rfl
#align category_theory.pseudofunctor.to_oplax_map₂ CategoryTheory.Pseudofunctor.to_oplax_map₂
+#print CategoryTheory.Pseudofunctor.to_oplax_mapId /-
@[simp]
theorem to_oplax_mapId (a : B) : (F : OplaxFunctor B C).map_id a = (F.map_id a).Hom :=
rfl
#align category_theory.pseudofunctor.to_oplax_map_id CategoryTheory.Pseudofunctor.to_oplax_mapId
+-/
+#print CategoryTheory.Pseudofunctor.to_oplax_mapComp /-
@[simp]
theorem to_oplax_mapComp {a b c : B} (f : a ⟶ b) (g : b ⟶ c) :
(F : OplaxFunctor B C).map_comp f g = (F.map_comp f g).Hom :=
rfl
#align category_theory.pseudofunctor.to_oplax_map_comp CategoryTheory.Pseudofunctor.to_oplax_mapComp
+-/
+#print CategoryTheory.Pseudofunctor.mapFunctor /-
/-- Function on 1-morphisms as a functor. -/
@[simps]
def mapFunctor (a b : B) : (a ⟶ b) ⥤ (F.obj a ⟶ F.obj b) :=
(F : OplaxFunctor B C).mapFunctor a b
#align category_theory.pseudofunctor.map_functor CategoryTheory.Pseudofunctor.mapFunctor
+-/
#print CategoryTheory.Pseudofunctor.id /-
/-- The identity pseudofunctor. -/
@@ -568,6 +578,7 @@ def mkOfOplax (F : OplaxFunctor B C) (F' : F.PseudoCore) : Pseudofunctor B C :=
#align category_theory.pseudofunctor.mk_of_oplax CategoryTheory.Pseudofunctor.mkOfOplax
-/
+#print CategoryTheory.Pseudofunctor.mkOfOplax' /-
/-- Construct a pseudofunctor from an oplax functor whose `map_id` and `map_comp` are isomorphisms.
-/
@[simps]
@@ -588,6 +599,7 @@ noncomputable def mkOfOplax' (F : OplaxFunctor B C) [∀ a, IsIso (F.map_id a)]
rw [is_iso.eq_comp_inv, ← inv_whisker_left, is_iso.eq_comp_inv]
simp only [assoc, F.map₂_associator] }
#align category_theory.pseudofunctor.mk_of_oplax' CategoryTheory.Pseudofunctor.mkOfOplax'
+-/
end
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -86,8 +86,8 @@ variable {D : Type u₃} [Quiver.{v₃ + 1} D] [∀ a b : D, Quiver.{w₃ + 1} (
1-morphisms, and 2-morphisms. This structure will be extended to define `oplax_functor`.
-/
structure PrelaxFunctor (B : Type u₁) [Quiver.{v₁ + 1} B] [∀ a b : B, Quiver.{w₁ + 1} (a ⟶ b)]
- (C : Type u₂) [Quiver.{v₂ + 1} C] [∀ a b : C, Quiver.{w₂ + 1} (a ⟶ b)] extends
- Prefunctor B C where
+ (C : Type u₂) [Quiver.{v₂ + 1} C] [∀ a b : C, Quiver.{w₂ + 1} (a ⟶ b)] extends
+ Prefunctor B C where
zipWith {a b : B} {f g : a ⟶ b} : (f ⟶ g) → (map f ⟶ map g)
#align category_theory.prelax_functor CategoryTheory.PrelaxFunctor
-/
@@ -178,7 +178,7 @@ associator, the left unitor, and the right unitor modulo some adjustments of dom
of 2-morphisms.
-/
structure OplaxFunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u₂)
- [Bicategory.{w₂, v₂} C] extends PrelaxFunctor B C where
+ [Bicategory.{w₂, v₂} C] extends PrelaxFunctor B C where
map_id (a : B) : map (𝟙 a) ⟶ 𝟙 (obj a)
map_comp {a b c : B} (f : a ⟶ b) (g : b ⟶ c) : map (f ≫ g) ⟶ map f ≫ map g
mapComp_naturality_left :
@@ -227,8 +227,8 @@ restate_axiom map₂_right_unitor'
attribute [simp] map_comp_naturality_left map_comp_naturality_right map₂_id map₂_associator
-attribute [reassoc]
- map_comp_naturality_left map_comp_naturality_right map₂_comp map₂_associator map₂_left_unitor map₂_right_unitor
+attribute [reassoc] map_comp_naturality_left map_comp_naturality_right map₂_comp map₂_associator
+ map₂_left_unitor map₂_right_unitor
attribute [simp] map₂_comp map₂_left_unitor map₂_right_unitor
@@ -378,7 +378,7 @@ associator, the left unitor, and the right unitor modulo some adjustments of dom
of 2-morphisms.
-/
structure Pseudofunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u₂)
- [Bicategory.{w₂, v₂} C] extends PrelaxFunctor B C where
+ [Bicategory.{w₂, v₂} C] extends PrelaxFunctor B C where
map_id (a : B) : map (𝟙 a) ≅ 𝟙 (obj a)
map_comp {a b c : B} (f : a ⟶ b) (g : b ⟶ c) : map (f ≫ g) ≅ map f ≫ map g
map₂_id : ∀ {a b : B} (f : a ⟶ b), map₂ (𝟙 f) = 𝟙 (map f) := by obviously
@@ -425,11 +425,11 @@ restate_axiom map₂_left_unitor'
restate_axiom map₂_right_unitor'
-attribute [reassoc]
- map₂_comp map₂_whisker_left map₂_whisker_right map₂_associator map₂_left_unitor map₂_right_unitor
+attribute [reassoc] map₂_comp map₂_whisker_left map₂_whisker_right map₂_associator map₂_left_unitor
+ map₂_right_unitor
-attribute [simp]
- map₂_id map₂_comp map₂_whisker_left map₂_whisker_right map₂_associator map₂_left_unitor map₂_right_unitor
+attribute [simp] map₂_id map₂_comp map₂_whisker_left map₂_whisker_right map₂_associator
+ map₂_left_unitor map₂_right_unitor
section
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -105,26 +105,20 @@ instance hasCoeToPrefunctor : Coe (PrelaxFunctor B C) (Prefunctor B C) :=
variable (F : PrelaxFunctor B C)
-/- warning: category_theory.prelax_functor.to_prefunctor_eq_coe clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.prelax_functor.to_prefunctor_eq_coe [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] : F.toPrefunctor = F :=
+theorem toPrefunctor_eq_coe : F.toPrefunctor = F :=
rfl
-#align category_theory.prelax_functor.to_prefunctor_eq_coe [anonymous]
+#align category_theory.prelax_functor.to_prefunctor_eq_coe CategoryTheory.PrelaxFunctor.toPrefunctor_eq_coe
-/- warning: category_theory.prelax_functor.to_prefunctor_obj clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.prelax_functor.to_prefunctor_obj [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] : (F : Prefunctor B C).obj = F.obj :=
+theorem to_prefunctor_obj : (F : Prefunctor B C).obj = F.obj :=
rfl
-#align category_theory.prelax_functor.to_prefunctor_obj [anonymous]
+#align category_theory.prelax_functor.to_prefunctor_obj CategoryTheory.PrelaxFunctor.to_prefunctor_obj
-/- warning: category_theory.prelax_functor.to_prefunctor_map clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.prelax_functor.to_prefunctor_map [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] : @Prefunctor.map B _ C _ F = @map _ _ _ _ _ _ F :=
+theorem to_prefunctor_map : @Prefunctor.map B _ C _ F = @map _ _ _ _ _ _ F :=
rfl
-#align category_theory.prelax_functor.to_prefunctor_map [anonymous]
+#align category_theory.prelax_functor.to_prefunctor_map CategoryTheory.PrelaxFunctor.to_prefunctor_map
#print CategoryTheory.PrelaxFunctor.id /-
/-- The identity prelax functor. -/
@@ -155,8 +149,6 @@ variable {B : Type u₁} [Bicategory.{w₁, v₁} B] {C : Type u₂} [Bicategory
variable {D : Type u₃} [Bicategory.{w₃, v₃} D]
-/- warning: category_theory.oplax_functor.map₂_associator_aux clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.map₂_associator_aux [anonymous]ₓ'. -/
/-
We use this auxiliary definition instead of writing it directly in the definition
of oplax functors because doing so will cause a timeout.
@@ -165,13 +157,13 @@ of oplax functors because doing so will cause a timeout.
modulo some adjustments of domains and codomains of 2-morphisms.
-/
@[simp]
-def [anonymous] (obj : B → C) (map : ∀ {X Y : B}, (X ⟶ Y) → (obj X ⟶ obj Y))
+def OplaxFunctor.Map₂AssociatorAux (obj : B → C) (map : ∀ {X Y : B}, (X ⟶ Y) → (obj X ⟶ obj Y))
(map₂ : ∀ {a b : B} {f g : a ⟶ b}, (f ⟶ g) → (map f ⟶ map g))
(map_comp : ∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), map (f ≫ g) ⟶ map f ≫ map g) {a b c d : B}
(f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d) : Prop :=
map₂ (α_ f g h).Hom ≫ map_comp f (g ≫ h) ≫ map f ◁ map_comp g h =
map_comp (f ≫ g) h ≫ map_comp f g ▷ map h ≫ (α_ (map f) (map g) (map h)).Hom
-#align category_theory.oplax_functor.map₂_associator_aux [anonymous]
+#align category_theory.oplax_functor.map₂_associator_aux CategoryTheory.OplaxFunctor.Map₂AssociatorAux
#print CategoryTheory.OplaxFunctor /-
/-- An oplax functor `F` between bicategories `B` and `C` consists of a function between objects
@@ -203,7 +195,8 @@ structure OplaxFunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u
obviously
map₂_associator :
∀ {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d),
- [anonymous] obj (fun _ _ => map) (fun a b f g => map₂) (fun a b c => map_comp) f g h := by
+ OplaxFunctor.Map₂AssociatorAux obj (fun _ _ => map) (fun a b f g => map₂)
+ (fun a b c => map_comp) f g h := by
obviously
map₂_leftUnitor :
∀ {a b : B} (f : a ⟶ b),
@@ -252,31 +245,25 @@ instance hasCoeToPrelax : Coe (OplaxFunctor B C) (PrelaxFunctor B C) :=
variable (F : OplaxFunctor B C)
-/- warning: category_theory.oplax_functor.to_prelax_eq_coe clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.to_prelax_eq_coe [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] : F.toPrelaxFunctor = F :=
+theorem to_prelax_eq_coe : F.toPrelaxFunctor = F :=
rfl
-#align category_theory.oplax_functor.to_prelax_eq_coe [anonymous]
+#align category_theory.oplax_functor.to_prelax_eq_coe CategoryTheory.OplaxFunctor.to_prelax_eq_coe
-/- warning: category_theory.oplax_functor.to_prelax_functor_obj clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.to_prelax_functor_obj [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] : (F : PrelaxFunctor B C).obj = F.obj :=
+theorem to_prelaxFunctor_obj : (F : PrelaxFunctor B C).obj = F.obj :=
rfl
-#align category_theory.oplax_functor.to_prelax_functor_obj [anonymous]
+#align category_theory.oplax_functor.to_prelax_functor_obj CategoryTheory.OplaxFunctor.to_prelaxFunctor_obj
@[simp]
theorem to_prelaxFunctor_map : @PrelaxFunctor.map B _ _ C _ _ F = @map _ _ _ _ F :=
rfl
#align category_theory.oplax_functor.to_prelax_functor_map CategoryTheory.OplaxFunctor.to_prelaxFunctor_map
-/- warning: category_theory.oplax_functor.to_prelax_functor_map₂ clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.to_prelax_functor_map₂ [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] : @PrelaxFunctor.map₂ B _ _ C _ _ F = @map₂ _ _ _ _ F :=
+theorem to_prelaxFunctor_map₂ : @PrelaxFunctor.map₂ B _ _ C _ _ F = @map₂ _ _ _ _ F :=
rfl
-#align category_theory.oplax_functor.to_prelax_functor_map₂ [anonymous]
+#align category_theory.oplax_functor.to_prelax_functor_map₂ CategoryTheory.OplaxFunctor.to_prelaxFunctor_map₂
/-- Function between 1-morphisms as a functor. -/
@[simps]
@@ -360,8 +347,6 @@ end
end OplaxFunctor
-/- warning: category_theory.pseudofunctor.map₂_associator_aux clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.map₂_associator_aux [anonymous]ₓ'. -/
/-
We use this auxiliary definition instead of writing it directly in the definition
of pseudofunctors because doing so will cause a timeout.
@@ -370,7 +355,7 @@ of pseudofunctors because doing so will cause a timeout.
modulo some adjustments of domains and codomains of 2-morphisms.
-/
@[simp]
-def [anonymous] (obj : B → C) (map : ∀ {X Y : B}, (X ⟶ Y) → (obj X ⟶ obj Y))
+def Pseudofunctor.Map₂AssociatorAux (obj : B → C) (map : ∀ {X Y : B}, (X ⟶ Y) → (obj X ⟶ obj Y))
(map₂ : ∀ {a b : B} {f g : a ⟶ b}, (f ⟶ g) → (map f ⟶ map g))
(map_comp : ∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), map (f ≫ g) ≅ map f ≫ map g) {a b c d : B}
(f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d) : Prop :=
@@ -378,7 +363,7 @@ def [anonymous] (obj : B → C) (map : ∀ {X Y : B}, (X ⟶ Y) → (obj X ⟶ o
(map_comp (f ≫ g) h).Hom ≫
(map_comp f g).Hom ▷ map h ≫
(α_ (map f) (map g) (map h)).Hom ≫ map f ◁ (map_comp g h).inv ≫ (map_comp f (g ≫ h)).inv
-#align category_theory.pseudofunctor.map₂_associator_aux [anonymous]
+#align category_theory.pseudofunctor.map₂_associator_aux CategoryTheory.Pseudofunctor.Map₂AssociatorAux
#print CategoryTheory.Pseudofunctor /-
/-- A pseudofunctor `F` between bicategories `B` and `C` consists of a function between objects
@@ -410,7 +395,8 @@ structure Pseudofunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u
obviously
map₂_associator :
∀ {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d),
- [anonymous] obj (fun a b => map) (fun a b f g => map₂) (fun a b c => map_comp) f g h := by
+ Pseudofunctor.Map₂AssociatorAux obj (fun a b => map) (fun a b f g => map₂)
+ (fun a b c => map_comp) f g h := by
obviously
map₂_leftUnitor :
∀ {a b : B} (f : a ⟶ b),
@@ -460,33 +446,25 @@ instance hasCoeToPrelaxFunctor : Coe (Pseudofunctor B C) (PrelaxFunctor B C) :=
variable (F : Pseudofunctor B C)
-/- warning: category_theory.pseudofunctor.to_prelax_functor_eq_coe clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_prelax_functor_eq_coe [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] : F.toPrelaxFunctor = F :=
+theorem toPrelaxFunctor_eq_coe : F.toPrelaxFunctor = F :=
rfl
-#align category_theory.pseudofunctor.to_prelax_functor_eq_coe [anonymous]
+#align category_theory.pseudofunctor.to_prelax_functor_eq_coe CategoryTheory.Pseudofunctor.toPrelaxFunctor_eq_coe
-/- warning: category_theory.pseudofunctor.to_prelax_functor_obj clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_prelax_functor_obj [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] : (F : PrelaxFunctor B C).obj = F.obj :=
+theorem to_prelaxFunctor_obj : (F : PrelaxFunctor B C).obj = F.obj :=
rfl
-#align category_theory.pseudofunctor.to_prelax_functor_obj [anonymous]
+#align category_theory.pseudofunctor.to_prelax_functor_obj CategoryTheory.Pseudofunctor.to_prelaxFunctor_obj
-/- warning: category_theory.pseudofunctor.to_prelax_functor_map clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_prelax_functor_map [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] : @PrelaxFunctor.map B _ _ C _ _ F = @map _ _ _ _ F :=
+theorem to_prelaxFunctor_map : @PrelaxFunctor.map B _ _ C _ _ F = @map _ _ _ _ F :=
rfl
-#align category_theory.pseudofunctor.to_prelax_functor_map [anonymous]
+#align category_theory.pseudofunctor.to_prelax_functor_map CategoryTheory.Pseudofunctor.to_prelaxFunctor_map
-/- warning: category_theory.pseudofunctor.to_prelax_functor_map₂ clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_prelax_functor_map₂ [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] : @PrelaxFunctor.map₂ B _ _ C _ _ F = @map₂ _ _ _ _ F :=
+theorem to_prelaxFunctor_map₂ : @PrelaxFunctor.map₂ B _ _ C _ _ F = @map₂ _ _ _ _ F :=
rfl
-#align category_theory.pseudofunctor.to_prelax_functor_map₂ [anonymous]
+#align category_theory.pseudofunctor.to_prelax_functor_map₂ CategoryTheory.Pseudofunctor.to_prelaxFunctor_map₂
#print CategoryTheory.Pseudofunctor.toOplax /-
/-- The oplax functor associated with a pseudofunctor. -/
@@ -503,31 +481,25 @@ instance hasCoeToOplax : Coe (Pseudofunctor B C) (OplaxFunctor B C) :=
#align category_theory.pseudofunctor.has_coe_to_oplax CategoryTheory.Pseudofunctor.hasCoeToOplax
-/
-/- warning: category_theory.pseudofunctor.to_oplax_eq_coe clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_oplax_eq_coe [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] : F.toOplax = F :=
+theorem toOplax_eq_coe : F.toOplax = F :=
rfl
-#align category_theory.pseudofunctor.to_oplax_eq_coe [anonymous]
+#align category_theory.pseudofunctor.to_oplax_eq_coe CategoryTheory.Pseudofunctor.toOplax_eq_coe
@[simp]
theorem to_oplax_obj : (F : OplaxFunctor B C).obj = F.obj :=
rfl
#align category_theory.pseudofunctor.to_oplax_obj CategoryTheory.Pseudofunctor.to_oplax_obj
-/- warning: category_theory.pseudofunctor.to_oplax_map clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_oplax_map [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] : @OplaxFunctor.map B _ C _ F = @map _ _ _ _ F :=
+theorem to_oplax_map : @OplaxFunctor.map B _ C _ F = @map _ _ _ _ F :=
rfl
-#align category_theory.pseudofunctor.to_oplax_map [anonymous]
+#align category_theory.pseudofunctor.to_oplax_map CategoryTheory.Pseudofunctor.to_oplax_map
-/- warning: category_theory.pseudofunctor.to_oplax_map₂ clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_oplax_map₂ [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] : @OplaxFunctor.map₂ B _ C _ F = @map₂ _ _ _ _ F :=
+theorem to_oplax_map₂ : @OplaxFunctor.map₂ B _ C _ F = @map₂ _ _ _ _ F :=
rfl
-#align category_theory.pseudofunctor.to_oplax_map₂ [anonymous]
+#align category_theory.pseudofunctor.to_oplax_map₂ CategoryTheory.Pseudofunctor.to_oplax_map₂
@[simp]
theorem to_oplax_mapId (a : B) : (F : OplaxFunctor B C).map_id a = (F.map_id a).Hom :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -69,7 +69,7 @@ namespace CategoryTheory
open Category Bicategory
-open Bicategory
+open scoped Bicategory
universe w₁ w₂ w₃ v₁ v₂ v₃ u₁ u₂ u₃
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -106,11 +106,6 @@ instance hasCoeToPrefunctor : Coe (PrelaxFunctor B C) (Prefunctor B C) :=
variable (F : PrelaxFunctor B C)
/- warning: category_theory.prelax_functor.to_prefunctor_eq_coe clashes with [anonymous] -> [anonymous]
-warning: category_theory.prelax_functor.to_prefunctor_eq_coe -> [anonymous] is a dubious translation:
-lean 3 declaration is
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- forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
Case conversion may be inaccurate. Consider using '#align category_theory.prelax_functor.to_prefunctor_eq_coe [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] : F.toPrefunctor = F :=
@@ -118,11 +113,6 @@ theorem [anonymous] : F.toPrefunctor = F :=
#align category_theory.prelax_functor.to_prefunctor_eq_coe [anonymous]
/- warning: category_theory.prelax_functor.to_prefunctor_obj clashes with [anonymous] -> [anonymous]
-warning: category_theory.prelax_functor.to_prefunctor_obj -> [anonymous] is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.prelax_functor.to_prefunctor_obj [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] : (F : Prefunctor B C).obj = F.obj :=
@@ -130,8 +120,6 @@ theorem [anonymous] : (F : Prefunctor B C).obj = F.obj :=
#align category_theory.prelax_functor.to_prefunctor_obj [anonymous]
/- warning: category_theory.prelax_functor.to_prefunctor_map clashes with [anonymous] -> [anonymous]
-warning: category_theory.prelax_functor.to_prefunctor_map -> [anonymous] is a dubious translation:
-<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.prelax_functor.to_prefunctor_map [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] : @Prefunctor.map B _ C _ F = @map _ _ _ _ _ _ F :=
@@ -168,11 +156,6 @@ variable {B : Type u₁} [Bicategory.{w₁, v₁} B] {C : Type u₂} [Bicategory
variable {D : Type u₃} [Bicategory.{w₃, v₃} D]
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Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.map₂_associator_aux [anonymous]ₓ'. -/
/-
We use this auxiliary definition instead of writing it directly in the definition
@@ -270,11 +253,6 @@ instance hasCoeToPrelax : Coe (OplaxFunctor B C) (PrelaxFunctor B C) :=
variable (F : OplaxFunctor B C)
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Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.to_prelax_eq_coe [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] : F.toPrelaxFunctor = F :=
@@ -282,11 +260,6 @@ theorem [anonymous] : F.toPrelaxFunctor = F :=
#align category_theory.oplax_functor.to_prelax_eq_coe [anonymous]
/- warning: category_theory.oplax_functor.to_prelax_functor_obj clashes with [anonymous] -> [anonymous]
-warning: category_theory.oplax_functor.to_prelax_functor_obj -> [anonymous] is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.to_prelax_functor_obj [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] : (F : PrelaxFunctor B C).obj = F.obj :=
@@ -299,20 +272,12 @@ theorem to_prelaxFunctor_map : @PrelaxFunctor.map B _ _ C _ _ F = @map _ _ _ _ F
#align category_theory.oplax_functor.to_prelax_functor_map CategoryTheory.OplaxFunctor.to_prelaxFunctor_map
/- warning: category_theory.oplax_functor.to_prelax_functor_map₂ clashes with [anonymous] -> [anonymous]
-warning: category_theory.oplax_functor.to_prelax_functor_map₂ -> [anonymous] is a dubious translation:
-<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.to_prelax_functor_map₂ [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] : @PrelaxFunctor.map₂ B _ _ C _ _ F = @map₂ _ _ _ _ F :=
rfl
#align category_theory.oplax_functor.to_prelax_functor_map₂ [anonymous]
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-Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.map_functor CategoryTheory.OplaxFunctor.mapFunctorₓ'. -/
/-- Function between 1-morphisms as a functor. -/
@[simps]
def mapFunctor (a b : B) : (a ⟶ b) ⥤ (F.obj a ⟶ F.obj b)
@@ -396,11 +361,6 @@ end
end OplaxFunctor
/- warning: category_theory.pseudofunctor.map₂_associator_aux clashes with [anonymous] -> [anonymous]
-warning: category_theory.pseudofunctor.map₂_associator_aux -> [anonymous] is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.map₂_associator_aux [anonymous]ₓ'. -/
/-
We use this auxiliary definition instead of writing it directly in the definition
@@ -501,11 +461,6 @@ instance hasCoeToPrelaxFunctor : Coe (Pseudofunctor B C) (PrelaxFunctor B C) :=
variable (F : Pseudofunctor B C)
/- warning: category_theory.pseudofunctor.to_prelax_functor_eq_coe clashes with [anonymous] -> [anonymous]
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Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_prelax_functor_eq_coe [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] : F.toPrelaxFunctor = F :=
@@ -513,11 +468,6 @@ theorem [anonymous] : F.toPrelaxFunctor = F :=
#align category_theory.pseudofunctor.to_prelax_functor_eq_coe [anonymous]
/- warning: category_theory.pseudofunctor.to_prelax_functor_obj clashes with [anonymous] -> [anonymous]
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@[simp]
theorem [anonymous] : (F : PrelaxFunctor B C).obj = F.obj :=
@@ -525,8 +475,6 @@ theorem [anonymous] : (F : PrelaxFunctor B C).obj = F.obj :=
#align category_theory.pseudofunctor.to_prelax_functor_obj [anonymous]
/- warning: category_theory.pseudofunctor.to_prelax_functor_map clashes with [anonymous] -> [anonymous]
-warning: category_theory.pseudofunctor.to_prelax_functor_map -> [anonymous] is a dubious translation:
-<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_prelax_functor_map [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] : @PrelaxFunctor.map B _ _ C _ _ F = @map _ _ _ _ F :=
@@ -534,8 +482,6 @@ theorem [anonymous] : @PrelaxFunctor.map B _ _ C _ _ F = @map _ _ _ _ F :=
#align category_theory.pseudofunctor.to_prelax_functor_map [anonymous]
/- warning: category_theory.pseudofunctor.to_prelax_functor_map₂ clashes with [anonymous] -> [anonymous]
-warning: category_theory.pseudofunctor.to_prelax_functor_map₂ -> [anonymous] is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_prelax_functor_map₂ [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] : @PrelaxFunctor.map₂ B _ _ C _ _ F = @map₂ _ _ _ _ F :=
@@ -558,34 +504,18 @@ instance hasCoeToOplax : Coe (Pseudofunctor B C) (OplaxFunctor B C) :=
-/
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@[simp]
theorem [anonymous] : F.toOplax = F :=
rfl
#align category_theory.pseudofunctor.to_oplax_eq_coe [anonymous]
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@[simp]
theorem to_oplax_obj : (F : OplaxFunctor B C).obj = F.obj :=
rfl
#align category_theory.pseudofunctor.to_oplax_obj CategoryTheory.Pseudofunctor.to_oplax_obj
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@[simp]
theorem [anonymous] : @OplaxFunctor.map B _ C _ F = @map _ _ _ _ F :=
@@ -593,37 +523,23 @@ theorem [anonymous] : @OplaxFunctor.map B _ C _ F = @map _ _ _ _ F :=
#align category_theory.pseudofunctor.to_oplax_map [anonymous]
/- warning: category_theory.pseudofunctor.to_oplax_map₂ clashes with [anonymous] -> [anonymous]
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Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_oplax_map₂ [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] : @OplaxFunctor.map₂ B _ C _ F = @map₂ _ _ _ _ F :=
rfl
#align category_theory.pseudofunctor.to_oplax_map₂ [anonymous]
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@[simp]
theorem to_oplax_mapId (a : B) : (F : OplaxFunctor B C).map_id a = (F.map_id a).Hom :=
rfl
#align category_theory.pseudofunctor.to_oplax_map_id CategoryTheory.Pseudofunctor.to_oplax_mapId
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@[simp]
theorem to_oplax_mapComp {a b c : B} (f : a ⟶ b) (g : b ⟶ c) :
(F : OplaxFunctor B C).map_comp f g = (F.map_comp f g).Hom :=
rfl
#align category_theory.pseudofunctor.to_oplax_map_comp CategoryTheory.Pseudofunctor.to_oplax_mapComp
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-Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.map_functor CategoryTheory.Pseudofunctor.mapFunctorₓ'. -/
/-- Function on 1-morphisms as a functor. -/
@[simps]
def mapFunctor (a b : B) : (a ⟶ b) ⥤ (F.obj a ⟶ F.obj b) :=
@@ -680,9 +596,6 @@ def mkOfOplax (F : OplaxFunctor B C) (F' : F.PseudoCore) : Pseudofunctor B C :=
#align category_theory.pseudofunctor.mk_of_oplax CategoryTheory.Pseudofunctor.mkOfOplax
-/
-/- warning: category_theory.pseudofunctor.mk_of_oplax' -> CategoryTheory.Pseudofunctor.mkOfOplax' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.mk_of_oplax' CategoryTheory.Pseudofunctor.mkOfOplax'ₓ'. -/
/-- Construct a pseudofunctor from an oplax functor whose `map_id` and `map_comp` are isomorphisms.
-/
@[simps]
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -131,10 +131,7 @@ theorem [anonymous] : (F : Prefunctor B C).obj = F.obj :=
/- warning: category_theory.prelax_functor.to_prefunctor_map clashes with [anonymous] -> [anonymous]
warning: category_theory.prelax_functor.to_prefunctor_map -> [anonymous] is a dubious translation:
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@[simp]
theorem [anonymous] : @Prefunctor.map B _ C _ F = @map _ _ _ _ _ _ F :=
@@ -303,10 +300,7 @@ theorem to_prelaxFunctor_map : @PrelaxFunctor.map B _ _ C _ _ F = @map _ _ _ _ F
/- warning: category_theory.oplax_functor.to_prelax_functor_map₂ clashes with [anonymous] -> [anonymous]
warning: category_theory.oplax_functor.to_prelax_functor_map₂ -> [anonymous] is a dubious translation:
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-but is expected to have type
- forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.to_prelax_functor_map₂ [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] : @PrelaxFunctor.map₂ B _ _ C _ _ F = @map₂ _ _ _ _ F :=
@@ -532,10 +526,7 @@ theorem [anonymous] : (F : PrelaxFunctor B C).obj = F.obj :=
/- warning: category_theory.pseudofunctor.to_prelax_functor_map clashes with [anonymous] -> [anonymous]
warning: category_theory.pseudofunctor.to_prelax_functor_map -> [anonymous] is a dubious translation:
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-but is expected to have type
- forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_prelax_functor_map [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] : @PrelaxFunctor.map B _ _ C _ _ F = @map _ _ _ _ F :=
@@ -544,10 +535,7 @@ theorem [anonymous] : @PrelaxFunctor.map B _ _ C _ _ F = @map _ _ _ _ F :=
/- warning: category_theory.pseudofunctor.to_prelax_functor_map₂ clashes with [anonymous] -> [anonymous]
warning: category_theory.pseudofunctor.to_prelax_functor_map₂ -> [anonymous] is a dubious translation:
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- forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_prelax_functor_map₂ [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] : @PrelaxFunctor.map₂ B _ _ C _ _ F = @map₂ _ _ _ _ F :=
@@ -606,10 +594,7 @@ theorem [anonymous] : @OplaxFunctor.map B _ C _ F = @map _ _ _ _ F :=
/- warning: category_theory.pseudofunctor.to_oplax_map₂ clashes with [anonymous] -> [anonymous]
warning: category_theory.pseudofunctor.to_oplax_map₂ -> [anonymous] is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_oplax_map₂ [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] : @OplaxFunctor.map₂ B _ C _ F = @map₂ _ _ _ _ F :=
@@ -617,10 +602,7 @@ theorem [anonymous] : @OplaxFunctor.map₂ B _ C _ F = @map₂ _ _ _ _ F :=
#align category_theory.pseudofunctor.to_oplax_map₂ [anonymous]
/- warning: category_theory.pseudofunctor.to_oplax_map_id -> CategoryTheory.Pseudofunctor.to_oplax_mapId is a dubious translation:
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C _inst_2 a b))) (CategoryTheory.Pseudofunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) a)) (CategoryTheory.Pseudofunctor.mapId.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a))
+<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_oplax_map_id CategoryTheory.Pseudofunctor.to_oplax_mapIdₓ'. -/
@[simp]
theorem to_oplax_mapId (a : B) : (F : OplaxFunctor B C).map_id a = (F.map_id a).Hom :=
@@ -628,10 +610,7 @@ theorem to_oplax_mapId (a : B) : (F : OplaxFunctor B C).map_id a = (F.map_id a).
#align category_theory.pseudofunctor.to_oplax_map_id CategoryTheory.Pseudofunctor.to_oplax_mapId
/- warning: category_theory.pseudofunctor.to_oplax_map_comp -> CategoryTheory.Pseudofunctor.to_oplax_mapComp is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_oplax_map_comp CategoryTheory.Pseudofunctor.to_oplax_mapCompₓ'. -/
@[simp]
theorem to_oplax_mapComp {a b c : B} (f : a ⟶ b) (g : b ⟶ c) :
@@ -702,10 +681,7 @@ def mkOfOplax (F : OplaxFunctor B C) (F' : F.PseudoCore) : Pseudofunctor B C :=
-/
/- warning: category_theory.pseudofunctor.mk_of_oplax' -> CategoryTheory.Pseudofunctor.mkOfOplax' is a dubious translation:
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u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) a)) (Prefunctor.map.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) a a (CategoryTheory.CategoryStruct.id.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1) a)) (CategoryTheory.CategoryStruct.id.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) a)) (CategoryTheory.OplaxFunctor.mapId.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a)] [_inst_5 : forall {a : B} {b : B} {c : B} (f : Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (g : Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) b c), CategoryTheory.IsIso.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) a) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) c)) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ 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(CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) c)) (Prefunctor.map.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, 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(CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) a c (CategoryTheory.CategoryStruct.comp.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1) a b c f g)) (CategoryTheory.CategoryStruct.comp.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B 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(CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) b) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) c) (Prefunctor.map.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) a b f) (Prefunctor.map.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => 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u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) b c g)) (CategoryTheory.OplaxFunctor.mapComp.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a b c f g)], CategoryTheory.Pseudofunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2
+<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.mk_of_oplax' CategoryTheory.Pseudofunctor.mkOfOplax'ₓ'. -/
/-- Construct a pseudofunctor from an oplax functor whose `map_id` and `map_comp` are isomorphisms.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -254,7 +254,7 @@ restate_axiom map₂_right_unitor'
attribute [simp] map_comp_naturality_left map_comp_naturality_right map₂_id map₂_associator
-attribute [reassoc.1]
+attribute [reassoc]
map_comp_naturality_left map_comp_naturality_right map₂_comp map₂_associator map₂_left_unitor map₂_right_unitor
attribute [simp] map₂_comp map₂_left_unitor map₂_right_unitor
@@ -485,7 +485,7 @@ restate_axiom map₂_left_unitor'
restate_axiom map₂_right_unitor'
-attribute [reassoc.1]
+attribute [reassoc]
map₂_comp map₂_whisker_left map₂_whisker_right map₂_associator map₂_left_unitor map₂_right_unitor
attribute [simp]
mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
! This file was ported from Lean 3 source module category_theory.bicategory.functor
-! leanprover-community/mathlib commit 3d7987cda72abc473c7cdbbb075170e9ac620042
+! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.CategoryTheory.Bicategory.Basic
/-!
# Oplax functors and pseudofunctors
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
An oplax functor `F` between bicategories `B` and `C` consists of
* a function between objects `F.obj : B ⟶ C`,
* a family of functions between 1-morphisms `F.map : (a ⟶ b) → (F.obj a ⟶ F.obj b)`,
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -78,6 +78,7 @@ variable {C : Type u₂} [Quiver.{v₂ + 1} C] [∀ a b : C, Quiver.{w₂ + 1} (
variable {D : Type u₃} [Quiver.{v₃ + 1} D] [∀ a b : D, Quiver.{w₃ + 1} (a ⟶ b)]
+#print CategoryTheory.PrelaxFunctor /-
/-- A prelax functor between bicategories consists of functions between objects,
1-morphisms, and 2-morphisms. This structure will be extended to define `oplax_functor`.
-/
@@ -86,47 +87,75 @@ structure PrelaxFunctor (B : Type u₁) [Quiver.{v₁ + 1} B] [∀ a b : B, Quiv
Prefunctor B C where
zipWith {a b : B} {f g : a ⟶ b} : (f ⟶ g) → (map f ⟶ map g)
#align category_theory.prelax_functor CategoryTheory.PrelaxFunctor
+-/
/-- The prefunctor between the underlying quivers. -/
add_decl_doc prelax_functor.to_prefunctor
namespace PrelaxFunctor
+#print CategoryTheory.PrelaxFunctor.hasCoeToPrefunctor /-
instance hasCoeToPrefunctor : Coe (PrelaxFunctor B C) (Prefunctor B C) :=
⟨toPrefunctor⟩
#align category_theory.prelax_functor.has_coe_to_prefunctor CategoryTheory.PrelaxFunctor.hasCoeToPrefunctor
+-/
variable (F : PrelaxFunctor B C)
+/- warning: category_theory.prelax_functor.to_prefunctor_eq_coe clashes with [anonymous] -> [anonymous]
+warning: category_theory.prelax_functor.to_prefunctor_eq_coe -> [anonymous] is a dubious translation:
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+but is expected to have type
+ forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align category_theory.prelax_functor.to_prefunctor_eq_coe [anonymous]ₓ'. -/
@[simp]
-theorem toPrefunctor_eq_coe : F.toPrefunctor = F :=
+theorem [anonymous] : F.toPrefunctor = F :=
rfl
-#align category_theory.prelax_functor.to_prefunctor_eq_coe CategoryTheory.PrelaxFunctor.toPrefunctor_eq_coe
-
+#align category_theory.prelax_functor.to_prefunctor_eq_coe [anonymous]
+
+/- warning: category_theory.prelax_functor.to_prefunctor_obj clashes with [anonymous] -> [anonymous]
+warning: category_theory.prelax_functor.to_prefunctor_obj -> [anonymous] is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.prelax_functor.to_prefunctor_obj [anonymous]ₓ'. -/
@[simp]
-theorem to_prefunctor_obj : (F : Prefunctor B C).obj = F.obj :=
+theorem [anonymous] : (F : Prefunctor B C).obj = F.obj :=
rfl
-#align category_theory.prelax_functor.to_prefunctor_obj CategoryTheory.PrelaxFunctor.to_prefunctor_obj
-
+#align category_theory.prelax_functor.to_prefunctor_obj [anonymous]
+
+/- warning: category_theory.prelax_functor.to_prefunctor_map clashes with [anonymous] -> [anonymous]
+warning: category_theory.prelax_functor.to_prefunctor_map -> [anonymous] is a dubious translation:
+lean 3 declaration is
+ forall {B : Type.{u₁}} [_inst_1 : Quiver.{succ v₁, u₁} B] [_inst_2 : forall (a : B) (b : B), Quiver.{succ w₁, v₁} (Quiver.Hom.{succ v₁, u₁} B _inst_1 a b)] {C : Type.{u₂}} [_inst_3 : Quiver.{succ v₂, u₂} C] [_inst_4 : forall (a : C) (b : C), Quiver.{succ w₂, v₂} (Quiver.Hom.{succ v₂, u₂} C _inst_3 a b)] (F : CategoryTheory.PrelaxFunctor.{w₁, w₂, v₁, v₂, u₁, u₂} B _inst_1 (fun (a : B) (b : B) => _inst_2 a b) C _inst_3 (fun (a : C) (b : C) => _inst_4 a b)), Eq.{max (succ u₁) (succ v₁) (succ v₂)} (forall {X : B} {Y : B}, (Quiver.Hom.{succ v₁, u₁} B _inst_1 X Y) -> (Quiver.Hom.{succ v₂, u₂} C _inst_3 (Prefunctor.obj.{succ v₁, succ v₂, u₁, u₂} B _inst_1 C _inst_3 ((fun (a : Sort.{max (succ u₁) (succ u₂) (succ v₁) (succ v₂) (succ w₁) (succ w₂)}) (b : Sort.{max (max (succ u₁) (succ v₁) (succ v₂)) (succ u₁) (succ u₂)}) [self : HasLiftT.{max (succ u₁) (succ u₂) (succ v₁) (succ v₂) (succ w₁) (succ w₂), max (max (succ u₁) (succ v₁) (succ v₂)) (succ u₁) (succ u₂)} a b] => self.0) 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B) (b : B) => _inst_2 a b) C _inst_3 (fun (a : C) (b : C) => _inst_4 a b))))) F)) (CategoryTheory.PrelaxFunctor.map.{w₁, w₂, v₁, v₂, u₁, u₂} B _inst_1 (fun (a : B) (b : B) => _inst_2 a b) C _inst_3 (fun (a : C) (b : C) => _inst_4 a b) F)
+but is expected to have type
+ forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align category_theory.prelax_functor.to_prefunctor_map [anonymous]ₓ'. -/
@[simp]
-theorem to_prefunctor_map : @Prefunctor.map B _ C _ F = @map _ _ _ _ _ _ F :=
+theorem [anonymous] : @Prefunctor.map B _ C _ F = @map _ _ _ _ _ _ F :=
rfl
-#align category_theory.prelax_functor.to_prefunctor_map CategoryTheory.PrelaxFunctor.to_prefunctor_map
+#align category_theory.prelax_functor.to_prefunctor_map [anonymous]
+#print CategoryTheory.PrelaxFunctor.id /-
/-- The identity prelax functor. -/
@[simps]
def id (B : Type u₁) [Quiver.{v₁ + 1} B] [∀ a b : B, Quiver.{w₁ + 1} (a ⟶ b)] : PrelaxFunctor B B :=
{ Prefunctor.id B with zipWith := fun a b f g η => η }
#align category_theory.prelax_functor.id CategoryTheory.PrelaxFunctor.id
+-/
instance : Inhabited (PrelaxFunctor B B) :=
⟨PrelaxFunctor.id B⟩
+#print CategoryTheory.PrelaxFunctor.comp /-
/-- Composition of prelax functors. -/
@[simps]
def comp (F : PrelaxFunctor B C) (G : PrelaxFunctor C D) : PrelaxFunctor B D :=
{ (F : Prefunctor B C).comp ↑G with zipWith := fun a b f g η => G.zipWith (F.zipWith η) }
#align category_theory.prelax_functor.comp CategoryTheory.PrelaxFunctor.comp
+-/
end PrelaxFunctor
@@ -138,6 +167,13 @@ variable {B : Type u₁} [Bicategory.{w₁, v₁} B] {C : Type u₂} [Bicategory
variable {D : Type u₃} [Bicategory.{w₃, v₃} D]
+/- warning: category_theory.oplax_functor.map₂_associator_aux clashes with [anonymous] -> [anonymous]
+warning: category_theory.oplax_functor.map₂_associator_aux -> [anonymous] is a dubious translation:
+lean 3 declaration is
+ forall {B : Type.{u₁}} [_inst_1 : CategoryTheory.Bicategory.{w₁, v₁, u₁} B] {C : Type.{u₂}} [_inst_2 : CategoryTheory.Bicategory.{w₂, v₂, u₂} C] (obj : B -> C) (map : forall {X : B} {Y : B}, (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) X Y) -> (Quiver.Hom.{succ v₂, u₂} C (CategoryTheory.CategoryStruct.toQuiver.{v₂, u₂} C (CategoryTheory.Bicategory.toCategoryStruct.{w₂, v₂, u₂} C _inst_2)) (obj X) (obj Y))), (forall {a : B} {b : B} {f : Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b} {g : Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b}, (Quiver.Hom.{succ w₁, v₁} (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b) (CategoryTheory.CategoryStruct.toQuiver.{w₁, v₁} (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{w₁, v₁} (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{w₁, v₁, u₁} B _inst_1 a b))) f g) -> (Quiver.Hom.{succ w₂, v₂} (Quiver.Hom.{succ v₂, u₂} C (CategoryTheory.CategoryStruct.toQuiver.{v₂, u₂} C (CategoryTheory.Bicategory.toCategoryStruct.{w₂, v₂, u₂} C _inst_2)) (obj a) (obj b)) (CategoryTheory.CategoryStruct.toQuiver.{w₂, v₂} (Quiver.Hom.{succ v₂, u₂} C (CategoryTheory.CategoryStruct.toQuiver.{v₂, u₂} C (CategoryTheory.Bicategory.toCategoryStruct.{w₂, v₂, u₂} C _inst_2)) (obj a) (obj b)) (CategoryTheory.Category.toCategoryStruct.{w₂, v₂} (Quiver.Hom.{succ v₂, u₂} C (CategoryTheory.CategoryStruct.toQuiver.{v₂, u₂} C (CategoryTheory.Bicategory.toCategoryStruct.{w₂, v₂, u₂} C _inst_2)) (obj a) (obj b)) (CategoryTheory.Bicategory.homCategory.{w₂, v₂, u₂} C _inst_2 (obj a) (obj b)))) (map a b f) (map a b g))) -> (forall {a : B} {b : B} {c : B} (f : Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b) (g : Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) b c), Quiver.Hom.{succ w₂, v₂} (Quiver.Hom.{succ v₂, u₂} C (CategoryTheory.CategoryStruct.toQuiver.{v₂, u₂} C (CategoryTheory.Bicategory.toCategoryStruct.{w₂, v₂, u₂} C _inst_2)) (obj a) (obj c)) (CategoryTheory.CategoryStruct.toQuiver.{w₂, v₂} (Quiver.Hom.{succ v₂, u₂} C (CategoryTheory.CategoryStruct.toQuiver.{v₂, u₂} C (CategoryTheory.Bicategory.toCategoryStruct.{w₂, v₂, u₂} C _inst_2)) (obj a) (obj c)) (CategoryTheory.Category.toCategoryStruct.{w₂, v₂} (Quiver.Hom.{succ v₂, u₂} C (CategoryTheory.CategoryStruct.toQuiver.{v₂, u₂} C (CategoryTheory.Bicategory.toCategoryStruct.{w₂, v₂, u₂} C _inst_2)) (obj a) (obj c)) (CategoryTheory.Bicategory.homCategory.{w₂, v₂, u₂} C _inst_2 (obj a) (obj c)))) (map a c (CategoryTheory.CategoryStruct.comp.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1) a b c f g)) (CategoryTheory.CategoryStruct.comp.{v₂, u₂} C (CategoryTheory.Bicategory.toCategoryStruct.{w₂, v₂, u₂} C _inst_2) (obj a) (obj b) (obj c) (map a b f) (map b c g))) -> (forall {a : B} {b : B} {c : B} {d : B}, (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b) -> (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) b c) -> (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) c d) -> Prop)
+but is expected to have type
+ forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.map₂_associator_aux [anonymous]ₓ'. -/
/-
We use this auxiliary definition instead of writing it directly in the definition
of oplax functors because doing so will cause a timeout.
@@ -146,14 +182,15 @@ of oplax functors because doing so will cause a timeout.
modulo some adjustments of domains and codomains of 2-morphisms.
-/
@[simp]
-def OplaxFunctor.Map₂AssociatorAux (obj : B → C) (map : ∀ {X Y : B}, (X ⟶ Y) → (obj X ⟶ obj Y))
+def [anonymous] (obj : B → C) (map : ∀ {X Y : B}, (X ⟶ Y) → (obj X ⟶ obj Y))
(map₂ : ∀ {a b : B} {f g : a ⟶ b}, (f ⟶ g) → (map f ⟶ map g))
(map_comp : ∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), map (f ≫ g) ⟶ map f ≫ map g) {a b c d : B}
(f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d) : Prop :=
map₂ (α_ f g h).Hom ≫ map_comp f (g ≫ h) ≫ map f ◁ map_comp g h =
map_comp (f ≫ g) h ≫ map_comp f g ▷ map h ≫ (α_ (map f) (map g) (map h)).Hom
-#align category_theory.oplax_functor.map₂_associator_aux CategoryTheory.OplaxFunctor.Map₂AssociatorAux
+#align category_theory.oplax_functor.map₂_associator_aux [anonymous]
+#print CategoryTheory.OplaxFunctor /-
/-- An oplax functor `F` between bicategories `B` and `C` consists of a function between objects
`F.obj`, a function between 1-morphisms `F.map`, and a function between 2-morphisms `F.map₂`.
@@ -169,32 +206,32 @@ structure OplaxFunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u
[Bicategory.{w₂, v₂} C] extends PrelaxFunctor B C where
map_id (a : B) : map (𝟙 a) ⟶ 𝟙 (obj a)
map_comp {a b c : B} (f : a ⟶ b) (g : b ⟶ c) : map (f ≫ g) ⟶ map f ≫ map g
- mapComp_naturality_left' :
+ mapComp_naturality_left :
∀ {a b c : B} {f f' : a ⟶ b} (η : f ⟶ f') (g : b ⟶ c),
map₂ (η ▷ g) ≫ map_comp f' g = map_comp f g ≫ map₂ η ▷ map g := by
obviously
- mapComp_naturality_right' :
+ mapComp_naturality_right :
∀ {a b c : B} (f : a ⟶ b) {g g' : b ⟶ c} (η : g ⟶ g'),
map₂ (f ◁ η) ≫ map_comp f g' = map_comp f g ≫ map f ◁ map₂ η := by
obviously
- map₂_id' : ∀ {a b : B} (f : a ⟶ b), map₂ (𝟙 f) = 𝟙 (map f) := by obviously
- map₂_comp' :
+ map₂_id : ∀ {a b : B} (f : a ⟶ b), map₂ (𝟙 f) = 𝟙 (map f) := by obviously
+ map₂_comp :
∀ {a b : B} {f g h : a ⟶ b} (η : f ⟶ g) (θ : g ⟶ h), map₂ (η ≫ θ) = map₂ η ≫ map₂ θ := by
obviously
- map₂_associator' :
+ map₂_associator :
∀ {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d),
- OplaxFunctor.Map₂AssociatorAux obj (fun _ _ => map) (fun a b f g => map₂)
- (fun a b c => map_comp) f g h := by
+ [anonymous] obj (fun _ _ => map) (fun a b f g => map₂) (fun a b c => map_comp) f g h := by
obviously
- map₂_left_unitor' :
+ map₂_leftUnitor :
∀ {a b : B} (f : a ⟶ b),
map₂ (λ_ f).Hom = map_comp (𝟙 a) f ≫ map_id a ▷ map f ≫ (λ_ (map f)).Hom := by
obviously
- map₂_right_unitor' :
+ map₂_rightUnitor :
∀ {a b : B} (f : a ⟶ b),
map₂ (ρ_ f).Hom = map_comp f (𝟙 b) ≫ map f ◁ map_id b ≫ (ρ_ (map f)).Hom := by
obviously
#align category_theory.oplax_functor CategoryTheory.OplaxFunctor
+-/
namespace OplaxFunctor
@@ -224,32 +261,61 @@ section
/-- The prelax functor between the underlying quivers. -/
add_decl_doc oplax_functor.to_prelax_functor
+#print CategoryTheory.OplaxFunctor.hasCoeToPrelax /-
instance hasCoeToPrelax : Coe (OplaxFunctor B C) (PrelaxFunctor B C) :=
⟨toPrelaxFunctor⟩
#align category_theory.oplax_functor.has_coe_to_prelax CategoryTheory.OplaxFunctor.hasCoeToPrelax
+-/
variable (F : OplaxFunctor B C)
+/- warning: category_theory.oplax_functor.to_prelax_eq_coe clashes with [anonymous] -> [anonymous]
+warning: category_theory.oplax_functor.to_prelax_eq_coe -> [anonymous] is a dubious translation:
+lean 3 declaration is
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C _inst_2 a b)))) (CategoryTheory.OplaxFunctor.hasCoeToPrelax.{w₁, w₂, v₁, v₂, u₁, u₂} B _inst_1 C _inst_2)))) F)
+but is expected to have type
+ forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.to_prelax_eq_coe [anonymous]ₓ'. -/
@[simp]
-theorem to_prelax_eq_coe : F.toPrelaxFunctor = F :=
+theorem [anonymous] : F.toPrelaxFunctor = F :=
rfl
-#align category_theory.oplax_functor.to_prelax_eq_coe CategoryTheory.OplaxFunctor.to_prelax_eq_coe
-
+#align category_theory.oplax_functor.to_prelax_eq_coe [anonymous]
+
+/- warning: category_theory.oplax_functor.to_prelax_functor_obj clashes with [anonymous] -> [anonymous]
+warning: category_theory.oplax_functor.to_prelax_functor_obj -> [anonymous] is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.OplaxFunctor.obj.{w₁, w₂, v₁, v₂, u₁, u₂} B _inst_1 C _inst_2 F)
+but is expected to have type
+ forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.to_prelax_functor_obj [anonymous]ₓ'. -/
@[simp]
-theorem to_prelaxFunctor_obj : (F : PrelaxFunctor B C).obj = F.obj :=
+theorem [anonymous] : (F : PrelaxFunctor B C).obj = F.obj :=
rfl
-#align category_theory.oplax_functor.to_prelax_functor_obj CategoryTheory.OplaxFunctor.to_prelaxFunctor_obj
+#align category_theory.oplax_functor.to_prelax_functor_obj [anonymous]
@[simp]
theorem to_prelaxFunctor_map : @PrelaxFunctor.map B _ _ C _ _ F = @map _ _ _ _ F :=
rfl
#align category_theory.oplax_functor.to_prelax_functor_map CategoryTheory.OplaxFunctor.to_prelaxFunctor_map
+/- warning: category_theory.oplax_functor.to_prelax_functor_map₂ clashes with [anonymous] -> [anonymous]
+warning: category_theory.oplax_functor.to_prelax_functor_map₂ -> [anonymous] is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.to_prelax_functor_map₂ [anonymous]ₓ'. -/
@[simp]
-theorem to_prelaxFunctor_map₂ : @PrelaxFunctor.map₂ B _ _ C _ _ F = @map₂ _ _ _ _ F :=
+theorem [anonymous] : @PrelaxFunctor.map₂ B _ _ C _ _ F = @map₂ _ _ _ _ F :=
rfl
-#align category_theory.oplax_functor.to_prelax_functor_map₂ CategoryTheory.OplaxFunctor.to_prelaxFunctor_map₂
-
+#align category_theory.oplax_functor.to_prelax_functor_map₂ [anonymous]
+
+/- warning: category_theory.oplax_functor.map_functor -> CategoryTheory.OplaxFunctor.mapFunctor is a dubious translation:
+lean 3 declaration is
+ forall {B : Type.{u5}} [_inst_1 : CategoryTheory.Bicategory.{u1, u3, u5} B] {C : Type.{u6}} [_inst_2 : CategoryTheory.Bicategory.{u2, u4, u6} C] (F : CategoryTheory.OplaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2) (a : B) (b : B), CategoryTheory.Functor.{u1, u2, u3, u4} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b) (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a) (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F b)) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a) (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F b))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.oplax_functor.map_functor CategoryTheory.OplaxFunctor.mapFunctorₓ'. -/
/-- Function between 1-morphisms as a functor. -/
@[simps]
def mapFunctor (a b : B) : (a ⟶ b) ⥤ (F.obj a ⟶ F.obj b)
@@ -258,6 +324,7 @@ def mapFunctor (a b : B) : (a ⟶ b) ⥤ (F.obj a ⟶ F.obj b)
map f g η := F.zipWith η
#align category_theory.oplax_functor.map_functor CategoryTheory.OplaxFunctor.mapFunctor
+#print CategoryTheory.OplaxFunctor.id /-
/-- The identity oplax functor. -/
@[simps]
def id (B : Type u₁) [Bicategory.{w₁, v₁} B] : OplaxFunctor B B :=
@@ -265,10 +332,12 @@ def id (B : Type u₁) [Bicategory.{w₁, v₁} B] : OplaxFunctor B B :=
map_id := fun a => 𝟙 (𝟙 a)
map_comp := fun a b c f g => 𝟙 (f ≫ g) }
#align category_theory.oplax_functor.id CategoryTheory.OplaxFunctor.id
+-/
instance : Inhabited (OplaxFunctor B B) :=
⟨id B⟩
+#print CategoryTheory.OplaxFunctor.comp /-
/-- Composition of oplax functors. -/
@[simps]
def comp (F : OplaxFunctor B C) (G : OplaxFunctor C D) : OplaxFunctor B D :=
@@ -278,32 +347,34 @@ def comp (F : OplaxFunctor B C) (G : OplaxFunctor C D) : OplaxFunctor B D :=
map_id := fun a => (G.mapFunctor _ _).map (F.map_id a) ≫ G.map_id (F.obj a)
map_comp := fun a b c f g =>
(G.mapFunctor _ _).map (F.map_comp f g) ≫ G.map_comp (F.map f) (F.map g)
- mapComp_naturality_left' := fun a b c f f' η g =>
+ mapComp_naturality_left := fun a b c f f' η g =>
by
dsimp
rw [← map₂_comp_assoc, map_comp_naturality_left, map₂_comp_assoc, map_comp_naturality_left,
assoc]
- mapComp_naturality_right' := fun a b c f g g' η =>
+ mapComp_naturality_right := fun a b c f g g' η =>
by
dsimp
rw [← map₂_comp_assoc, map_comp_naturality_right, map₂_comp_assoc, map_comp_naturality_right,
assoc]
- map₂_associator' := fun a b c d f g h => by
+ map₂_associator := fun a b c d f g h => by
dsimp
simp only [map₂_associator, ← map₂_comp_assoc, ← map_comp_naturality_right_assoc,
whisker_left_comp, assoc]
simp only [map₂_associator, map₂_comp, map_comp_naturality_left_assoc, comp_whisker_right,
assoc]
- map₂_left_unitor' := fun a b f => by
+ map₂_leftUnitor := fun a b f => by
dsimp
simp only [map₂_left_unitor, map₂_comp, map_comp_naturality_left_assoc, comp_whisker_right,
assoc]
- map₂_right_unitor' := fun a b f => by
+ map₂_rightUnitor := fun a b f => by
dsimp
simp only [map₂_right_unitor, map₂_comp, map_comp_naturality_right_assoc, whisker_left_comp,
assoc] }
#align category_theory.oplax_functor.comp CategoryTheory.OplaxFunctor.comp
+-/
+#print CategoryTheory.OplaxFunctor.PseudoCore /-
/-- A structure on an oplax functor that promotes an oplax functor to a pseudofunctor.
See `pseudofunctor.mk_of_oplax`.
-/
@@ -315,6 +386,7 @@ structure PseudoCore (F : OplaxFunctor B C) where
mapCompIso_hom' :
∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), (map_comp_iso f g).Hom = F.map_comp f g := by obviously
#align category_theory.oplax_functor.pseudo_core CategoryTheory.OplaxFunctor.PseudoCore
+-/
restate_axiom pseudo_core.map_id_iso_hom'
@@ -326,6 +398,13 @@ end
end OplaxFunctor
+/- warning: category_theory.pseudofunctor.map₂_associator_aux clashes with [anonymous] -> [anonymous]
+warning: category_theory.pseudofunctor.map₂_associator_aux -> [anonymous] is a dubious translation:
+lean 3 declaration is
+ forall {B : Type.{u₁}} [_inst_1 : CategoryTheory.Bicategory.{w₁, v₁, u₁} B] {C : Type.{u₂}} [_inst_2 : CategoryTheory.Bicategory.{w₂, v₂, u₂} C] (obj : B -> C) (map : forall {X : B} {Y : B}, (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) X Y) -> (Quiver.Hom.{succ v₂, u₂} C (CategoryTheory.CategoryStruct.toQuiver.{v₂, u₂} C (CategoryTheory.Bicategory.toCategoryStruct.{w₂, v₂, u₂} C _inst_2)) (obj X) (obj Y))), (forall {a : B} {b : B} {f : Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b} {g : Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b}, (Quiver.Hom.{succ w₁, v₁} (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b) (CategoryTheory.CategoryStruct.toQuiver.{w₁, v₁} (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{w₁, v₁} (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{w₁, v₁, u₁} B _inst_1 a b))) f g) -> (Quiver.Hom.{succ w₂, v₂} (Quiver.Hom.{succ v₂, u₂} C (CategoryTheory.CategoryStruct.toQuiver.{v₂, u₂} C (CategoryTheory.Bicategory.toCategoryStruct.{w₂, v₂, u₂} C _inst_2)) (obj a) (obj b)) (CategoryTheory.CategoryStruct.toQuiver.{w₂, v₂} (Quiver.Hom.{succ v₂, u₂} C (CategoryTheory.CategoryStruct.toQuiver.{v₂, u₂} C (CategoryTheory.Bicategory.toCategoryStruct.{w₂, v₂, u₂} C _inst_2)) (obj a) (obj b)) (CategoryTheory.Category.toCategoryStruct.{w₂, v₂} (Quiver.Hom.{succ v₂, u₂} C (CategoryTheory.CategoryStruct.toQuiver.{v₂, u₂} C (CategoryTheory.Bicategory.toCategoryStruct.{w₂, v₂, u₂} C _inst_2)) (obj a) (obj b)) (CategoryTheory.Bicategory.homCategory.{w₂, v₂, u₂} C _inst_2 (obj a) (obj b)))) (map a b f) (map a b g))) -> (forall {a : B} {b : B} {c : B} (f : Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b) (g : Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) b c), CategoryTheory.Iso.{w₂, v₂} (Quiver.Hom.{succ v₂, u₂} C (CategoryTheory.CategoryStruct.toQuiver.{v₂, u₂} C (CategoryTheory.Bicategory.toCategoryStruct.{w₂, v₂, u₂} C _inst_2)) (obj a) (obj c)) (CategoryTheory.Bicategory.homCategory.{w₂, v₂, u₂} C _inst_2 (obj a) (obj c)) (map a c (CategoryTheory.CategoryStruct.comp.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1) a b c f g)) (CategoryTheory.CategoryStruct.comp.{v₂, u₂} C (CategoryTheory.Bicategory.toCategoryStruct.{w₂, v₂, u₂} C _inst_2) (obj a) (obj b) (obj c) (map a b f) (map b c g))) -> (forall {a : B} {b : B} {c : B} {d : B}, (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b) -> (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) b c) -> (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) c d) -> Prop)
+but is expected to have type
+ forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.map₂_associator_aux [anonymous]ₓ'. -/
/-
We use this auxiliary definition instead of writing it directly in the definition
of pseudofunctors because doing so will cause a timeout.
@@ -334,7 +413,7 @@ of pseudofunctors because doing so will cause a timeout.
modulo some adjustments of domains and codomains of 2-morphisms.
-/
@[simp]
-def Pseudofunctor.Map₂AssociatorAux (obj : B → C) (map : ∀ {X Y : B}, (X ⟶ Y) → (obj X ⟶ obj Y))
+def [anonymous] (obj : B → C) (map : ∀ {X Y : B}, (X ⟶ Y) → (obj X ⟶ obj Y))
(map₂ : ∀ {a b : B} {f g : a ⟶ b}, (f ⟶ g) → (map f ⟶ map g))
(map_comp : ∀ {a b c : B} (f : a ⟶ b) (g : b ⟶ c), map (f ≫ g) ≅ map f ≫ map g) {a b c d : B}
(f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d) : Prop :=
@@ -342,8 +421,9 @@ def Pseudofunctor.Map₂AssociatorAux (obj : B → C) (map : ∀ {X Y : B}, (X
(map_comp (f ≫ g) h).Hom ≫
(map_comp f g).Hom ▷ map h ≫
(α_ (map f) (map g) (map h)).Hom ≫ map f ◁ (map_comp g h).inv ≫ (map_comp f (g ≫ h)).inv
-#align category_theory.pseudofunctor.map₂_associator_aux CategoryTheory.Pseudofunctor.Map₂AssociatorAux
+#align category_theory.pseudofunctor.map₂_associator_aux [anonymous]
+#print CategoryTheory.Pseudofunctor /-
/-- A pseudofunctor `F` between bicategories `B` and `C` consists of a function between objects
`F.obj`, a function between 1-morphisms `F.map`, and a function between 2-morphisms `F.map₂`.
@@ -359,8 +439,8 @@ structure Pseudofunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u
[Bicategory.{w₂, v₂} C] extends PrelaxFunctor B C where
map_id (a : B) : map (𝟙 a) ≅ 𝟙 (obj a)
map_comp {a b c : B} (f : a ⟶ b) (g : b ⟶ c) : map (f ≫ g) ≅ map f ≫ map g
- map₂_id' : ∀ {a b : B} (f : a ⟶ b), map₂ (𝟙 f) = 𝟙 (map f) := by obviously
- map₂_comp' :
+ map₂_id : ∀ {a b : B} (f : a ⟶ b), map₂ (𝟙 f) = 𝟙 (map f) := by obviously
+ map₂_comp :
∀ {a b : B} {f g h : a ⟶ b} (η : f ⟶ g) (θ : g ⟶ h), map₂ (η ≫ θ) = map₂ η ≫ map₂ θ := by
obviously
map₂_whisker_left' :
@@ -371,20 +451,20 @@ structure Pseudofunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u
∀ {a b c : B} {f g : a ⟶ b} (η : f ⟶ g) (h : b ⟶ c),
map₂ (η ▷ h) = (map_comp f h).Hom ≫ map₂ η ▷ map h ≫ (map_comp g h).inv := by
obviously
- map₂_associator' :
+ map₂_associator :
∀ {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d),
- Pseudofunctor.Map₂AssociatorAux obj (fun a b => map) (fun a b f g => map₂)
- (fun a b c => map_comp) f g h := by
+ [anonymous] obj (fun a b => map) (fun a b f g => map₂) (fun a b c => map_comp) f g h := by
obviously
- map₂_left_unitor' :
+ map₂_leftUnitor :
∀ {a b : B} (f : a ⟶ b),
map₂ (λ_ f).Hom = (map_comp (𝟙 a) f).Hom ≫ (map_id a).Hom ▷ map f ≫ (λ_ (map f)).Hom := by
obviously
- map₂_right_unitor' :
+ map₂_rightUnitor :
∀ {a b : B} (f : a ⟶ b),
map₂ (ρ_ f).Hom = (map_comp f (𝟙 b)).Hom ≫ map f ◁ (map_id b).Hom ≫ (ρ_ (map f)).Hom := by
obviously
#align category_theory.pseudofunctor CategoryTheory.Pseudofunctor
+-/
namespace Pseudofunctor
@@ -415,80 +495,160 @@ open Iso
/-- The prelax functor between the underlying quivers. -/
add_decl_doc pseudofunctor.to_prelax_functor
+#print CategoryTheory.Pseudofunctor.hasCoeToPrelaxFunctor /-
instance hasCoeToPrelaxFunctor : Coe (Pseudofunctor B C) (PrelaxFunctor B C) :=
⟨toPrelaxFunctor⟩
#align category_theory.pseudofunctor.has_coe_to_prelax_functor CategoryTheory.Pseudofunctor.hasCoeToPrelaxFunctor
+-/
variable (F : Pseudofunctor B C)
+/- warning: category_theory.pseudofunctor.to_prelax_functor_eq_coe clashes with [anonymous] -> [anonymous]
+warning: category_theory.pseudofunctor.to_prelax_functor_eq_coe -> [anonymous] is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_prelax_functor_eq_coe [anonymous]ₓ'. -/
@[simp]
-theorem toPrelaxFunctor_eq_coe : F.toPrelaxFunctor = F :=
+theorem [anonymous] : F.toPrelaxFunctor = F :=
rfl
-#align category_theory.pseudofunctor.to_prelax_functor_eq_coe CategoryTheory.Pseudofunctor.toPrelaxFunctor_eq_coe
-
+#align category_theory.pseudofunctor.to_prelax_functor_eq_coe [anonymous]
+
+/- warning: category_theory.pseudofunctor.to_prelax_functor_obj clashes with [anonymous] -> [anonymous]
+warning: category_theory.pseudofunctor.to_prelax_functor_obj -> [anonymous] is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_prelax_functor_obj [anonymous]ₓ'. -/
@[simp]
-theorem to_prelaxFunctor_obj : (F : PrelaxFunctor B C).obj = F.obj :=
+theorem [anonymous] : (F : PrelaxFunctor B C).obj = F.obj :=
rfl
-#align category_theory.pseudofunctor.to_prelax_functor_obj CategoryTheory.Pseudofunctor.to_prelaxFunctor_obj
-
+#align category_theory.pseudofunctor.to_prelax_functor_obj [anonymous]
+
+/- warning: category_theory.pseudofunctor.to_prelax_functor_map clashes with [anonymous] -> [anonymous]
+warning: category_theory.pseudofunctor.to_prelax_functor_map -> [anonymous] is a dubious translation:
+lean 3 declaration is
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F)
+but is expected to have type
+ forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_prelax_functor_map [anonymous]ₓ'. -/
@[simp]
-theorem to_prelaxFunctor_map : @PrelaxFunctor.map B _ _ C _ _ F = @map _ _ _ _ F :=
+theorem [anonymous] : @PrelaxFunctor.map B _ _ C _ _ F = @map _ _ _ _ F :=
rfl
-#align category_theory.pseudofunctor.to_prelax_functor_map CategoryTheory.Pseudofunctor.to_prelaxFunctor_map
-
+#align category_theory.pseudofunctor.to_prelax_functor_map [anonymous]
+
+/- warning: category_theory.pseudofunctor.to_prelax_functor_map₂ clashes with [anonymous] -> [anonymous]
+warning: category_theory.pseudofunctor.to_prelax_functor_map₂ -> [anonymous] is a dubious translation:
+lean 3 declaration is
+ forall {B : Type.{u₁}} [_inst_1 : CategoryTheory.Bicategory.{w₁, v₁, u₁} B] {C : Type.{u₂}} [_inst_2 : CategoryTheory.Bicategory.{w₂, v₂, u₂} C] (F : CategoryTheory.Pseudofunctor.{w₁, w₂, v₁, v₂, u₁, u₂} B _inst_1 C _inst_2), Eq.{max (succ u₁) (succ v₁) (succ w₁) (succ w₂)} (forall {a : B} {b : B} {f : Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b} {g : Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b}, (Quiver.Hom.{succ w₁, v₁} (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, u₁} B _inst_1)) a b) ((fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{w₁, v₁} (Quiver.Hom.{succ v₁, u₁} B (CategoryTheory.CategoryStruct.toQuiver.{v₁, u₁} B (CategoryTheory.Bicategory.toCategoryStruct.{w₁, v₁, 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+but is expected to have type
+ forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_prelax_functor_map₂ [anonymous]ₓ'. -/
@[simp]
-theorem to_prelaxFunctor_map₂ : @PrelaxFunctor.map₂ B _ _ C _ _ F = @map₂ _ _ _ _ F :=
+theorem [anonymous] : @PrelaxFunctor.map₂ B _ _ C _ _ F = @map₂ _ _ _ _ F :=
rfl
-#align category_theory.pseudofunctor.to_prelax_functor_map₂ CategoryTheory.Pseudofunctor.to_prelaxFunctor_map₂
+#align category_theory.pseudofunctor.to_prelax_functor_map₂ [anonymous]
+#print CategoryTheory.Pseudofunctor.toOplax /-
/-- The oplax functor associated with a pseudofunctor. -/
def toOplax : OplaxFunctor B C :=
{ (F : PrelaxFunctor B C) with
map_id := fun a => (F.map_id a).Hom
map_comp := fun a b c f g => (F.map_comp f g).Hom }
#align category_theory.pseudofunctor.to_oplax CategoryTheory.Pseudofunctor.toOplax
+-/
+#print CategoryTheory.Pseudofunctor.hasCoeToOplax /-
instance hasCoeToOplax : Coe (Pseudofunctor B C) (OplaxFunctor B C) :=
⟨toOplax⟩
#align category_theory.pseudofunctor.has_coe_to_oplax CategoryTheory.Pseudofunctor.hasCoeToOplax
+-/
+/- warning: category_theory.pseudofunctor.to_oplax_eq_coe clashes with [anonymous] -> [anonymous]
+warning: category_theory.pseudofunctor.to_oplax_eq_coe -> [anonymous] is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_oplax_eq_coe [anonymous]ₓ'. -/
@[simp]
-theorem toOplax_eq_coe : F.toOplax = F :=
+theorem [anonymous] : F.toOplax = F :=
rfl
-#align category_theory.pseudofunctor.to_oplax_eq_coe CategoryTheory.Pseudofunctor.toOplax_eq_coe
-
+#align category_theory.pseudofunctor.to_oplax_eq_coe [anonymous]
+
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+Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_oplax_obj CategoryTheory.Pseudofunctor.to_oplax_objₓ'. -/
@[simp]
theorem to_oplax_obj : (F : OplaxFunctor B C).obj = F.obj :=
rfl
#align category_theory.pseudofunctor.to_oplax_obj CategoryTheory.Pseudofunctor.to_oplax_obj
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_oplax_map [anonymous]ₓ'. -/
@[simp]
-theorem to_oplax_map : @OplaxFunctor.map B _ C _ F = @map _ _ _ _ F :=
+theorem [anonymous] : @OplaxFunctor.map B _ C _ F = @map _ _ _ _ F :=
rfl
-#align category_theory.pseudofunctor.to_oplax_map CategoryTheory.Pseudofunctor.to_oplax_map
-
+#align category_theory.pseudofunctor.to_oplax_map [anonymous]
+
+/- warning: category_theory.pseudofunctor.to_oplax_map₂ clashes with [anonymous] -> [anonymous]
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+but is expected to have type
+ forall {B : Type.{u}} {_inst_1 : Type.{v}}, (Nat -> B -> _inst_1) -> Nat -> (List.{u} B) -> (List.{v} _inst_1)
+Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_oplax_map₂ [anonymous]ₓ'. -/
@[simp]
-theorem to_oplax_map₂ : @OplaxFunctor.map₂ B _ C _ F = @map₂ _ _ _ _ F :=
+theorem [anonymous] : @OplaxFunctor.map₂ B _ C _ F = @map₂ _ _ _ _ F :=
rfl
-#align category_theory.pseudofunctor.to_oplax_map₂ CategoryTheory.Pseudofunctor.to_oplax_map₂
-
+#align category_theory.pseudofunctor.to_oplax_map₂ [anonymous]
+
+/- warning: category_theory.pseudofunctor.to_oplax_map_id -> CategoryTheory.Pseudofunctor.to_oplax_mapId is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_oplax_map_id CategoryTheory.Pseudofunctor.to_oplax_mapIdₓ'. -/
@[simp]
theorem to_oplax_mapId (a : B) : (F : OplaxFunctor B C).map_id a = (F.map_id a).Hom :=
rfl
#align category_theory.pseudofunctor.to_oplax_map_id CategoryTheory.Pseudofunctor.to_oplax_mapId
+/- warning: category_theory.pseudofunctor.to_oplax_map_comp -> CategoryTheory.Pseudofunctor.to_oplax_mapComp is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 (CategoryTheory.Pseudofunctor.toOplax.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F))) a) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 (CategoryTheory.Pseudofunctor.toOplax.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F))) c)) (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 (CategoryTheory.Pseudofunctor.toOplax.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F))) a) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 (CategoryTheory.Pseudofunctor.toOplax.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F))) c)) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 (CategoryTheory.Pseudofunctor.toOplax.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F))) a) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 (CategoryTheory.Pseudofunctor.toOplax.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F))) c)) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 (CategoryTheory.Pseudofunctor.toOplax.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F))) a) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 (CategoryTheory.Pseudofunctor.toOplax.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F))) c)))) (Prefunctor.map.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C 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(CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.Pseudofunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) b c g)) (CategoryTheory.Pseudofunctor.mapComp.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a b c f g))
+Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.to_oplax_map_comp CategoryTheory.Pseudofunctor.to_oplax_mapCompₓ'. -/
@[simp]
theorem to_oplax_mapComp {a b c : B} (f : a ⟶ b) (g : b ⟶ c) :
(F : OplaxFunctor B C).map_comp f g = (F.map_comp f g).Hom :=
rfl
#align category_theory.pseudofunctor.to_oplax_map_comp CategoryTheory.Pseudofunctor.to_oplax_mapComp
+/- warning: category_theory.pseudofunctor.map_functor -> CategoryTheory.Pseudofunctor.mapFunctor is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.Pseudofunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) b))
+Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.map_functor CategoryTheory.Pseudofunctor.mapFunctorₓ'. -/
/-- Function on 1-morphisms as a functor. -/
@[simps]
def mapFunctor (a b : B) : (a ⟶ b) ⥤ (F.obj a ⟶ F.obj b) :=
(F : OplaxFunctor B C).mapFunctor a b
#align category_theory.pseudofunctor.map_functor CategoryTheory.Pseudofunctor.mapFunctor
+#print CategoryTheory.Pseudofunctor.id /-
/-- The identity pseudofunctor. -/
@[simps]
def id (B : Type u₁) [Bicategory.{w₁, v₁} B] : Pseudofunctor B B :=
@@ -496,10 +656,12 @@ def id (B : Type u₁) [Bicategory.{w₁, v₁} B] : Pseudofunctor B B :=
map_id := fun a => Iso.refl (𝟙 a)
map_comp := fun a b c f g => Iso.refl (f ≫ g) }
#align category_theory.pseudofunctor.id CategoryTheory.Pseudofunctor.id
+-/
instance : Inhabited (Pseudofunctor B B) :=
⟨id B⟩
+#print CategoryTheory.Pseudofunctor.comp /-
/-- Composition of pseudofunctors. -/
@[simps]
def comp (F : Pseudofunctor B C) (G : Pseudofunctor C D) : Pseudofunctor B D :=
@@ -510,7 +672,9 @@ def comp (F : Pseudofunctor B C) (G : Pseudofunctor C D) : Pseudofunctor B D :=
map_comp := fun a b c f g =>
(G.mapFunctor _ _).mapIso (F.map_comp f g) ≪≫ G.map_comp (F.map f) (F.map g) }
#align category_theory.pseudofunctor.comp CategoryTheory.Pseudofunctor.comp
+-/
+#print CategoryTheory.Pseudofunctor.mkOfOplax /-
/-- Construct a pseudofunctor from an oplax functor whose `map_id` and `map_comp` are isomorphisms.
-/
@[simps]
@@ -526,13 +690,20 @@ def mkOfOplax (F : OplaxFunctor B C) (F' : F.PseudoCore) : Pseudofunctor B C :=
dsimp
rw [F'.map_comp_iso_hom f h, ← F.map_comp_naturality_left_assoc, ← F'.map_comp_iso_hom g h,
hom_inv_id, comp_id]
- map₂_associator' := fun a b c d f g h => by
+ map₂_associator := fun a b c d f g h => by
dsimp
rw [F'.map_comp_iso_hom (f ≫ g) h, F'.map_comp_iso_hom f g, ← F.map₂_associator_assoc, ←
F'.map_comp_iso_hom f (g ≫ h), ← F'.map_comp_iso_hom g h, hom_inv_whisker_left_assoc,
hom_inv_id, comp_id] }
#align category_theory.pseudofunctor.mk_of_oplax CategoryTheory.Pseudofunctor.mkOfOplax
+-/
+/- warning: category_theory.pseudofunctor.mk_of_oplax' -> CategoryTheory.Pseudofunctor.mkOfOplax' is a dubious translation:
+lean 3 declaration is
+ forall {B : Type.{u5}} [_inst_1 : CategoryTheory.Bicategory.{u1, u3, u5} B] {C : Type.{u6}} [_inst_2 : CategoryTheory.Bicategory.{u2, u4, u6} C] (F : CategoryTheory.OplaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2) [_inst_4 : forall (a : B), CategoryTheory.IsIso.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a) (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a)) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a) (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a)) (CategoryTheory.OplaxFunctor.map.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a a (CategoryTheory.CategoryStruct.id.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1) a)) (CategoryTheory.CategoryStruct.id.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2) (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a)) (CategoryTheory.OplaxFunctor.mapId.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a)] [_inst_5 : forall {a : B} {b : B} {c : B} (f : Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (g : Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) b c), CategoryTheory.IsIso.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a) (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F c)) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a) (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F c)) (CategoryTheory.OplaxFunctor.map.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a c (CategoryTheory.CategoryStruct.comp.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1) a b c f g)) (CategoryTheory.CategoryStruct.comp.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2) (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a) (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F b) (CategoryTheory.OplaxFunctor.obj.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F c) (CategoryTheory.OplaxFunctor.map.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a b f) (CategoryTheory.OplaxFunctor.map.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F b c g)) (CategoryTheory.OplaxFunctor.mapComp.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a b c f g)], CategoryTheory.Pseudofunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2
+but is expected to have type
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(CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) a a (CategoryTheory.CategoryStruct.id.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1) a)) (CategoryTheory.CategoryStruct.id.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) a)) (CategoryTheory.OplaxFunctor.mapId.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a)] [_inst_5 : forall {a : B} {b : B} {c : B} (f : Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (g : Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) b c), CategoryTheory.IsIso.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) a) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) c)) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ 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(CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) c)) (Prefunctor.map.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) a c (CategoryTheory.CategoryStruct.comp.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1) a b c f g)) (CategoryTheory.CategoryStruct.comp.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) a) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) b) (Prefunctor.obj.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) c) (Prefunctor.map.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) a b f) (Prefunctor.map.{succ u3, succ u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (CategoryTheory.PrelaxFunctor.toPrefunctor.{u1, u2, u3, u4, u5, u6} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) (fun (a : B) (b : B) => CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Quiver.Hom.{succ u3, u5} B (CategoryTheory.CategoryStruct.toQuiver.{u3, u5} B (CategoryTheory.Bicategory.toCategoryStruct.{u1, u3, u5} B _inst_1)) a b) (CategoryTheory.Bicategory.homCategory.{u1, u3, u5} B _inst_1 a b))) C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) (fun (a : C) (b : C) => CategoryTheory.CategoryStruct.toQuiver.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Category.toCategoryStruct.{u2, u4} (Quiver.Hom.{succ u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u6} C (CategoryTheory.Bicategory.toCategoryStruct.{u2, u4, u6} C _inst_2)) a b) (CategoryTheory.Bicategory.homCategory.{u2, u4, u6} C _inst_2 a b))) (CategoryTheory.OplaxFunctor.toPrelaxFunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F)) b c g)) (CategoryTheory.OplaxFunctor.mapComp.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2 F a b c f g)], CategoryTheory.Pseudofunctor.{u1, u2, u3, u4, u5, u6} B _inst_1 C _inst_2
+Case conversion may be inaccurate. Consider using '#align category_theory.pseudofunctor.mk_of_oplax' CategoryTheory.Pseudofunctor.mkOfOplax'ₓ'. -/
/-- Construct a pseudofunctor from an oplax functor whose `map_id` and `map_comp` are isomorphisms.
-/
@[simps]
@@ -547,7 +718,7 @@ noncomputable def mkOfOplax' (F : OplaxFunctor B C) [∀ a, IsIso (F.map_id a)]
map₂_whisker_right' := fun a b c f g η h => by
dsimp
rw [← assoc, is_iso.eq_comp_inv, F.map_comp_naturality_left]
- map₂_associator' := fun a b c d f g h => by
+ map₂_associator := fun a b c d f g h => by
dsimp
simp only [← assoc]
rw [is_iso.eq_comp_inv, ← inv_whisker_left, is_iso.eq_comp_inv]
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -313,8 +313,8 @@ def comp (F : OplaxFunctor B C) (G : OplaxFunctor C D) : OplaxFunctor B D :=
/-- A structure on an oplax functor that promotes an oplax functor to a pseudofunctor.
See `Pseudofunctor.mkOfOplax`.
-/
--- Porting note: removing no lint for nonempty_instance
---@[nolint has_nonempty_instance]
+-- Porting note(#5171): linter not ported yet
+-- @[nolint has_nonempty_instance]
-- Porting note: removing primes in structure name because
-- my understanding is that they're no longer needed
structure PseudoCore (F : OplaxFunctor B C) where
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -71,9 +71,7 @@ universe w₁ w₂ w₃ v₁ v₂ v₃ u₁ u₂ u₃
section
variable {B : Type u₁} [Quiver.{v₁ + 1} B] [∀ a b : B, Quiver.{w₁ + 1} (a ⟶ b)]
-
variable {C : Type u₂} [Quiver.{v₂ + 1} C] [∀ a b : C, Quiver.{w₂ + 1} (a ⟶ b)]
-
variable {D : Type u₃} [Quiver.{v₃ + 1} D] [∀ a b : D, Quiver.{w₃ + 1} (a ⟶ b)]
/-- A prelax functor between bicategories consists of functions between objects,
@@ -131,7 +129,6 @@ end
section
variable {B : Type u₁} [Bicategory.{w₁, v₁} B] {C : Type u₂} [Bicategory.{w₂, v₂} C]
-
variable {D : Type u₃} [Bicategory.{w₃, v₃} D]
-- Porting note: in Lean 3 the below auxiliary definition was only used once, in the definition
Includes some doc comments and real code: this is exhaustive, with two exceptions:
Follow-up to #11301, much shorter this time.
@@ -33,8 +33,8 @@ pseudofunctors can be defined by using the composition of oplax functors as foll
```lean
def comp (F : Pseudofunctor B C) (G : Pseudofunctor C D) : Pseudofunctor B D :=
mkOfOplax ((F : OplaxFunctor B C).comp G)
- { mapIdIso := λ a => (G.mapFunctor _ _).mapIso (F.mapId a) ≪≫ G.mapId (F.obj a),
- mapCompIso := λ f g =>
+ { mapIdIso := fun a ↦ (G.mapFunctor _ _).mapIso (F.mapId a) ≪≫ G.mapId (F.obj a),
+ mapCompIso := fun f g ↦
(G.mapFunctor _ _).mapIso (F.mapComp f g) ≪≫ G.mapComp (F.map f) (F.map g) }
```
although the composition of pseudofunctors in this file is defined by using the default constructor
Homogenises porting notes via capitalisation and addition of whitespace.
It makes the following changes:
@@ -101,7 +101,7 @@ instance hasCoeToPrefunctor : Coe (PrelaxFunctor B C) (Prefunctor B C) :=
variable (F : PrelaxFunctor B C)
--- porting note: deleted syntactic tautologies `toPrefunctor_eq_coe : F.toPrefunctor = F`
+-- Porting note: deleted syntactic tautologies `toPrefunctor_eq_coe : F.toPrefunctor = F`
-- and `to_prefunctor_obj : (F : Prefunctor B C).obj = F.obj`
-- and `to_prefunctor_map`
#noalign category_theory.prelax_functor.to_prefunctor_eq_coe
@@ -117,7 +117,7 @@ def id (B : Type u₁) [Quiver.{v₁ + 1} B] [∀ a b : B, Quiver.{w₁ + 1} (a
instance : Inhabited (PrelaxFunctor B B) :=
⟨PrelaxFunctor.id B⟩
--- porting note: `by exact` was not necessary in mathlib3
+-- Porting note: `by exact` was not necessary in mathlib3
/-- Composition of prelax functors. -/
@[simps]
def comp (F : PrelaxFunctor B C) (G : PrelaxFunctor C D) : PrelaxFunctor B D :=
@@ -134,7 +134,7 @@ variable {B : Type u₁} [Bicategory.{w₁, v₁} B] {C : Type u₂} [Bicategory
variable {D : Type u₃} [Bicategory.{w₃, v₃} D]
--- porting note: in Lean 3 the below auxiliary definition was only used once, in the definition
+-- Porting note: in Lean 3 the below auxiliary definition was only used once, in the definition
-- of oplax functor, with a comment that it had to be used to fix a timeout. The timeout is
-- not present in Lean 4, however Lean 4 is not as good at seeing through the definition,
-- meaning that `simp` wasn't functioning as well as it should. I have hence removed
@@ -174,7 +174,7 @@ structure OplaxFunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u
map₂_comp :
∀ {a b : B} {f g h : a ⟶ b} (η : f ⟶ g) (θ : g ⟶ h), map₂ (η ≫ θ) = map₂ η ≫ map₂ θ := by
aesop_cat
- -- porting note: `map₂_associator_aux` was used here in lean 3, but this was a hack
+ -- Porting note: `map₂_associator_aux` was used here in lean 3, but this was a hack
-- to avoid a timeout; we revert this hack here (because it was causing other problems
-- and was not necessary in lean 4)
map₂_associator :
@@ -212,11 +212,11 @@ namespace OplaxFunctor
/- Porting note: removed primes from field names and remove `restate_axiom` since
that is no longer needed in Lean 4 -/
--- porting note: more stuff was tagged `simp` here in lean 3 but `reassoc (attr := simp)`
+-- Porting note: more stuff was tagged `simp` here in lean 3 but `reassoc (attr := simp)`
-- is doing this job a couple of lines below this.
attribute [simp] map₂_id
--- porting note: was auto-ported as `attribute [reassoc.1]` for some reason
+-- Porting note: was auto-ported as `attribute [reassoc.1]` for some reason
attribute [reassoc (attr := simp)]
mapComp_naturality_left mapComp_naturality_right map₂_associator
@@ -245,16 +245,16 @@ instance hasCoeToPrelax : Coe (OplaxFunctor B C) (PrelaxFunctor B C) :=
variable (F : OplaxFunctor B C)
--- porting note: `to_prelax_eq_coe` and `to_prelaxFunctor_obj` are
+-- Porting note: `to_prelax_eq_coe` and `to_prelaxFunctor_obj` are
-- syntactic tautologies in lean 4
#noalign category_theory.oplax_functor.to_prelax_eq_coe
#noalign category_theory.oplax_functor.to_prelax_functor_obj
---porting note: removed lemma `to_prelaxFunctor_map` relating the now
+-- Porting note: removed lemma `to_prelaxFunctor_map` relating the now
-- nonexistent `PrelaxFunctor.map` and `OplaxFunctor.map`
#noalign CategoryTheory.OplaxFunctor.to_prelaxFunctor_map
---porting note: removed lemma `to_prelaxFunctor_map₂` relating
+-- Porting note: removed lemma `to_prelaxFunctor_map₂` relating
-- `PrelaxFunctor.map₂` to nonexistent `OplaxFunctor.map₂`
#noalign category_theory.oplax_functor.to_prelax_functor_map₂
@@ -297,7 +297,7 @@ def comp (F : OplaxFunctor B C) (G : OplaxFunctor C D) : OplaxFunctor B D :=
assoc]
map₂_associator := fun f g h => by
dsimp
- -- porting note: if you use the `map₂_associator_aux` hack in the definition of
+ -- Porting note: if you use the `map₂_associator_aux` hack in the definition of
-- `map₂_associator` then the `simp only` call below does not seem to apply `map₂_associator`
simp only [map₂_associator, ← map₂_comp_assoc, ← mapComp_naturality_right_assoc,
whiskerLeft_comp, assoc]
@@ -316,9 +316,9 @@ def comp (F : OplaxFunctor B C) (G : OplaxFunctor C D) : OplaxFunctor B D :=
/-- A structure on an oplax functor that promotes an oplax functor to a pseudofunctor.
See `Pseudofunctor.mkOfOplax`.
-/
--- porting note: removing no lint for nonempty_instance
+-- Porting note: removing no lint for nonempty_instance
--@[nolint has_nonempty_instance]
--- porting note: removing primes in structure name because
+-- Porting note: removing primes in structure name because
-- my understanding is that they're no longer needed
structure PseudoCore (F : OplaxFunctor B C) where
mapIdIso (a : B) : F.map (𝟙 a) ≅ 𝟙 (F.obj a)
@@ -339,7 +339,7 @@ end
end OplaxFunctor
--- porting note: this auxiliary def was introduced in Lean 3 and only used once, in this file,
+-- Porting note: this auxiliary def was introduced in Lean 3 and only used once, in this file,
-- to avoid a timeout. In Lean 4 the timeout isn't present and the definition causes other
-- things to break (simp proofs) so I removed it.
-- def Pseudofunctor.Map₂AssociatorAux (obj : B → C) (map : ∀ {X Y : B}, (X ⟶ Y) → (obj X ⟶ obj Y))
@@ -399,7 +399,7 @@ initialize_simps_projections Pseudofunctor (+toPrelaxFunctor, -obj, -map, -map
namespace Pseudofunctor
--- porting note: was `[reassoc.1]` for some reason?
+-- Porting note: was `[reassoc.1]` for some reason?
attribute [reassoc]
map₂_comp map₂_whisker_left map₂_whisker_right map₂_associator map₂_left_unitor map₂_right_unitor
@@ -431,16 +431,16 @@ instance hasCoeToPrelaxFunctor : Coe (Pseudofunctor B C) (PrelaxFunctor B C) :=
variable (F : Pseudofunctor B C)
--- porting note: `toPrelaxFunctor_eq_coe` and `to_prelaxFunctor_obj`
+-- Porting note: `toPrelaxFunctor_eq_coe` and `to_prelaxFunctor_obj`
-- are syntactic tautologies in lean 4
#noalign category_theory.pseudofunctor.to_prelax_functor_eq_coe
#noalign category_theory.pseudofunctor.to_prelax_functor_obj
---porting note: removed lemma `to_prelaxFunctor_map` relating the now
+-- Porting note: removed lemma `to_prelaxFunctor_map` relating the now
-- nonexistent `PrelaxFunctor.map` and the now nonexistent `Pseudofunctor.map`
#noalign category_theory.pseudofunctor.to_prelax_functor_map
---porting note: removed lemma `to_prelaxFunctor_map₂` relating
+-- Porting note: removed lemma `to_prelaxFunctor_map₂` relating
-- `PrelaxFunctor.map₂` to nonexistent `Pseudofunctor.map₂`
#noalign category_theory.pseudofunctor.to_prelax_functor_map₂
@@ -455,7 +455,7 @@ instance hasCoeToOplax : Coe (Pseudofunctor B C) (OplaxFunctor B C) :=
⟨toOplax⟩
#align category_theory.pseudofunctor.has_coe_to_oplax CategoryTheory.Pseudofunctor.hasCoeToOplax
--- porting note: `toOplax_eq_coe` is a syntactic tautology in lean 4
+-- Porting note: `toOplax_eq_coe` is a syntactic tautology in lean 4
#noalign category_theory.pseudofunctor.to_oplax_eq_coe
@[simp]
@@ -463,11 +463,11 @@ theorem to_oplax_obj : (F : OplaxFunctor B C).obj = F.obj :=
rfl
#align category_theory.pseudofunctor.to_oplax_obj CategoryTheory.Pseudofunctor.to_oplax_obj
--- porting note: to_oplax_map related `OplaxFunctor.map` to `Pseudofunctor.map` but neither
+-- Porting note: to_oplax_map related `OplaxFunctor.map` to `Pseudofunctor.map` but neither
-- of these exist
#noalign category_theory.pseudofunctor.to_oplax_map
--- porting note: to_oplax_map₂ related `OplaxFunctor.map₂` to `Pseudofunctor.map₂` but neither
+-- Porting note: to_oplax_map₂ related `OplaxFunctor.map₂` to `Pseudofunctor.map₂` but neither
-- of these exist
#noalign category_theory.pseudofunctor.to_oplax_map₂
@@ -482,7 +482,7 @@ theorem to_oplax_mapComp {a b c : B} (f : a ⟶ b) (g : b ⟶ c) :
rfl
#align category_theory.pseudofunctor.to_oplax_map_comp CategoryTheory.Pseudofunctor.to_oplax_mapComp
--- porting note: I changed `simps` to `simps!` without understanding what I was doing
+-- Porting note: I changed `simps` to `simps!` without understanding what I was doing
-- (lean 4 told me to do this)
/-- Function on 1-morphisms as a functor. -/
@[simps!]
@@ -530,7 +530,7 @@ def mkOfOplax (F : OplaxFunctor B C) (F' : F.PseudoCore) : Pseudofunctor B C :=
map₂_associator := fun f g h => by
dsimp
rw [F'.mapCompIso_hom (f ≫ g) h, F'.mapCompIso_hom f g, ← F.map₂_associator_assoc, ←
- F'.mapCompIso_hom f (g ≫ h), ← F'.mapCompIso_hom g h, hom_inv_whiskerLeft_assoc,
+ F'.mapCompIso_hom f (g ≫ h), ← F'.mapCompIso_hom g h, whiskerLeft_hom_inv_assoc,
hom_inv_id, comp_id] }
#align category_theory.pseudofunctor.mk_of_oplax CategoryTheory.Pseudofunctor.mkOfOplax
@@ -2,14 +2,11 @@
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-
-! This file was ported from Lean 3 source module category_theory.bicategory.functor
-! leanprover-community/mathlib commit 369525b73f229ccd76a6ec0e0e0bf2be57599768
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Bicategory.Basic
+#align_import category_theory.bicategory.functor from "leanprover-community/mathlib"@"369525b73f229ccd76a6ec0e0e0bf2be57599768"
+
/-!
# Oplax functors and pseudofunctors
@@ -35,10 +35,10 @@ of the oplax functor associated with it is already done. For example, the compos
pseudofunctors can be defined by using the composition of oplax functors as follows:
```lean
def comp (F : Pseudofunctor B C) (G : Pseudofunctor C D) : Pseudofunctor B D :=
-mkOfOplax ((F : OplaxFunctor B C).comp G)
-{ mapIdIso := λ a => (G.mapFunctor _ _).mapIso (F.mapId a) ≪≫ G.mapId (F.obj a),
- mapCompIso := λ f g =>
- (G.mapFunctor _ _).mapIso (F.mapComp f g) ≪≫ G.mapComp (F.map f) (F.map g) }
+ mkOfOplax ((F : OplaxFunctor B C).comp G)
+ { mapIdIso := λ a => (G.mapFunctor _ _).mapIso (F.mapId a) ≪≫ G.mapId (F.obj a),
+ mapCompIso := λ f g =>
+ (G.mapFunctor _ _).mapIso (F.mapComp f g) ≪≫ G.mapComp (F.map f) (F.map g) }
```
although the composition of pseudofunctors in this file is defined by using the default constructor
because `obviously` wasn't smart enough in mathlib3 and the porter of this file was too lazy
@@ -42,7 +42,7 @@ mkOfOplax ((F : OplaxFunctor B C).comp G)
```
although the composition of pseudofunctors in this file is defined by using the default constructor
because `obviously` wasn't smart enough in mathlib3 and the porter of this file was too lazy
-to investigage this issue further in mathlib4. Similarly, the composition is also defined by using
+to investigate this issue further in mathlib4. Similarly, the composition is also defined by using
`mkOfOplax'` after giving appropriate instances for `IsIso`. The former constructor
`mkOfOplax` requires isomorphisms as data type `Iso`, and so it is useful if you don't want
to forget the definitions of the inverses. On the other hand, the latter constructor
Now that leanprover/lean4#2210 has been merged, this PR:
set_option synthInstance.etaExperiment true
commands (and some etaExperiment%
term elaborators)set_option maxHeartbeats
commandsCo-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>
@@ -504,8 +504,6 @@ def id (B : Type u₁) [Bicategory.{w₁, v₁} B] : Pseudofunctor B B :=
instance : Inhabited (Pseudofunctor B B) :=
⟨id B⟩
--- porting note: this is aesop_cat taking a long time auto-filling in fields
-set_option maxHeartbeats 500000 in
/-- Composition of pseudofunctors. -/
@[simps]
def comp (F : Pseudofunctor B C) (G : Pseudofunctor C D) : Pseudofunctor B D :=
by
s! (#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 by
s".
@@ -289,13 +289,11 @@ def comp (F : OplaxFunctor B C) (G : OplaxFunctor C D) : OplaxFunctor B D :=
mapId := fun a => by exact (G.mapFunctor _ _).map (F.mapId a) ≫ G.mapId (F.obj a)
mapComp := fun f g => by
exact (G.mapFunctor _ _).map (F.mapComp f g) ≫ G.mapComp (F.map f) (F.map g)
- mapComp_naturality_left := fun η g =>
- by
+ mapComp_naturality_left := fun η g => by
dsimp
rw [← map₂_comp_assoc, mapComp_naturality_left, map₂_comp_assoc, mapComp_naturality_left,
assoc]
- mapComp_naturality_right := fun η =>
- by
+ mapComp_naturality_right := fun η => by
dsimp
intros
rw [← map₂_comp_assoc, mapComp_naturality_right, map₂_comp_assoc, mapComp_naturality_right,
This PR fixes two things:
align
statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align
). This is often seen in the mathport output after ending calc
blocks.#align
statements. (This was needed for a script I wrote for #3630.)@@ -100,8 +100,7 @@ attribute [coe] CategoryTheory.PrelaxFunctor.toPrefunctor
instance hasCoeToPrefunctor : Coe (PrelaxFunctor B C) (Prefunctor B C) :=
⟨toPrefunctor⟩
-#align category_theory.prelax_functor.has_coe_to_prefunctor
- CategoryTheory.PrelaxFunctor.hasCoeToPrefunctor
+#align category_theory.prelax_functor.has_coe_to_prefunctor CategoryTheory.PrelaxFunctor.hasCoeToPrefunctor
variable (F : PrelaxFunctor B C)
This fixes a regression of @[simps]
to @[simp]
from #2969, per zulip.
There are a few incidental changes to @[simps]
arguments in this PR, just removing arguments that had no effect on behaviour.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -85,13 +85,12 @@ variable {D : Type u₃} [Quiver.{v₃ + 1} D] [∀ a b : D, Quiver.{w₃ + 1} (
structure PrelaxFunctor (B : Type u₁) [Quiver.{v₁ + 1} B] [∀ a b : B, Quiver.{w₁ + 1} (a ⟶ b)]
(C : Type u₂) [Quiver.{v₂ + 1} C] [∀ a b : C, Quiver.{w₂ + 1} (a ⟶ b)] extends
Prefunctor B C where
+ /-- The action of a prelax functor on 2-morphisms. -/
map₂ {a b : B} {f g : a ⟶ b} : (f ⟶ g) → (map f ⟶ map g)
#align category_theory.prelax_functor CategoryTheory.PrelaxFunctor
initialize_simps_projections PrelaxFunctor (+toPrefunctor, -obj, -map)
-attribute [nolint docBlame] CategoryTheory.PrelaxFunctor.map₂
-
/-- The prefunctor between the underlying quivers. -/
add_decl_doc PrelaxFunctor.toPrefunctor
@@ -371,7 +370,7 @@ associator, the left unitor, and the right unitor modulo some adjustments of dom
of 2-morphisms.
-/
structure Pseudofunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u₂)
- [Bicategory.{w₂, v₂} C] extends PrelaxFunctor B C where
+ [Bicategory.{w₂, v₂} C] extends PrelaxFunctor B C where
mapId (a : B) : map (𝟙 a) ≅ 𝟙 (obj a)
mapComp {a b c : B} (f : a ⟶ b) (g : b ⟶ c) : map (f ≫ g) ≅ map f ≫ map g
map₂_id : ∀ {a b : B} (f : a ⟶ b), map₂ (𝟙 f) = 𝟙 (map f) := by aesop_cat
Apparently we have CI scripts that assume those fall on a single line. The command line used to fix the aligns was:
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^#align ([^[:space:]]+)\n *([^[:space:]]+)$/#align \1 \2/' {} \;
Co-authored-by: Moritz Firsching <firsching@google.com>
@@ -198,14 +198,10 @@ structure OplaxFunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u
#align category_theory.oplax_functor CategoryTheory.OplaxFunctor
#align category_theory.oplax_functor.map_id CategoryTheory.OplaxFunctor.mapId
#align category_theory.oplax_functor.map_comp CategoryTheory.OplaxFunctor.mapComp
-#align category_theory.oplax_functor.map_comp_naturality_left'
- CategoryTheory.OplaxFunctor.mapComp_naturality_left
-#align category_theory.oplax_functor.map_comp_naturality_left
- CategoryTheory.OplaxFunctor.mapComp_naturality_left
-#align category_theory.oplax_functor.map_comp_naturality_right'
- CategoryTheory.OplaxFunctor.mapComp_naturality_right
-#align category_theory.oplax_functor.map_comp_naturality_right
- CategoryTheory.OplaxFunctor.mapComp_naturality_right
+#align category_theory.oplax_functor.map_comp_naturality_left' CategoryTheory.OplaxFunctor.mapComp_naturality_left
+#align category_theory.oplax_functor.map_comp_naturality_left CategoryTheory.OplaxFunctor.mapComp_naturality_left
+#align category_theory.oplax_functor.map_comp_naturality_right' CategoryTheory.OplaxFunctor.mapComp_naturality_right
+#align category_theory.oplax_functor.map_comp_naturality_right CategoryTheory.OplaxFunctor.mapComp_naturality_right
#align category_theory.oplax_functor.map₂_id' CategoryTheory.OplaxFunctor.map₂_id
#align category_theory.oplax_functor.map₂_comp' CategoryTheory.OplaxFunctor.map₂_comp
#align category_theory.oplax_functor.map₂_associator' CategoryTheory.OplaxFunctor.map₂_associator
@@ -438,8 +434,7 @@ attribute [nolint docBlame] CategoryTheory.Pseudofunctor.mapId
instance hasCoeToPrelaxFunctor : Coe (Pseudofunctor B C) (PrelaxFunctor B C) :=
⟨toPrelaxFunctor⟩
-#align category_theory.pseudofunctor.has_coe_to_prelax_functor
- CategoryTheory.Pseudofunctor.hasCoeToPrelaxFunctor
+#align category_theory.pseudofunctor.has_coe_to_prelax_functor CategoryTheory.Pseudofunctor.hasCoeToPrelaxFunctor
variable (F : Pseudofunctor B C)
initialize_simps_projections
now by default generates all projections of all parent structures, and doesn't generate the projections to those parent structures.TwoPointed
)Internal changes:
ParsedProjectionData
to avoid the bug reported here (and to another bug where it seemed that the wrong data was inserted in ParsedProjectionData
, but it was hard to minimize because of all the crashes). If we manage to fix the bug in that Zulip thread, I'll see if I can track down the other bug in commit 97454284Co-authored-by: Johan Commelin <johan@commelin.net>
@@ -88,6 +88,8 @@ structure PrelaxFunctor (B : Type u₁) [Quiver.{v₁ + 1} B] [∀ a b : B, Quiv
map₂ {a b : B} {f g : a ⟶ b} : (f ⟶ g) → (map f ⟶ map g)
#align category_theory.prelax_functor CategoryTheory.PrelaxFunctor
+initialize_simps_projections PrelaxFunctor (+toPrefunctor, -obj, -map)
+
attribute [nolint docBlame] CategoryTheory.PrelaxFunctor.map₂
/-- The prefunctor between the underlying quivers. -/
@@ -212,6 +214,8 @@ structure OplaxFunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u
#align category_theory.oplax_functor.map₂_right_unitor CategoryTheory.OplaxFunctor.map₂_rightUnitor
#align category_theory.oplax_functor.map₂_right_unitor' CategoryTheory.OplaxFunctor.map₂_rightUnitor
+initialize_simps_projections OplaxFunctor (+toPrelaxFunctor, -obj, -map, -map₂)
+
namespace OplaxFunctor
/- Porting note: removed primes from field names and remove `restate_axiom` since
@@ -402,6 +406,8 @@ structure Pseudofunctor (B : Type u₁) [Bicategory.{w₁, v₁} B] (C : Type u
aesop_cat
#align category_theory.pseudofunctor CategoryTheory.Pseudofunctor
+initialize_simps_projections Pseudofunctor (+toPrelaxFunctor, -obj, -map, -map₂)
+
namespace Pseudofunctor
-- porting note: was `[reassoc.1]` for some reason?
All dependencies are ported!