category_theory.monoidal.types.coyoneda
⟷
Mathlib.CategoryTheory.Monoidal.Types.Coyoneda
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/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -40,7 +40,7 @@ def coyonedaTensorUnit (C : Type u) [Category.{v} C] [MonoidalCategory C] :
μ := fun X Y p => (λ_ (𝟙_ C)).inv ≫ (p.1 ⊗ p.2)
μ_natural' := by tidy
associativity' := fun X Y Z => by
- ext ⟨⟨f, g⟩, h⟩; dsimp at f g h
+ ext ⟨⟨f, g⟩, h⟩; dsimp at f g h
dsimp; simp only [iso.cancel_iso_inv_left, category.assoc]
conv_lhs =>
rw [← category.id_comp h, tensor_comp, category.assoc, associator_naturality, ←
@@ -48,7 +48,7 @@ def coyonedaTensorUnit (C : Type u) [Category.{v} C] [MonoidalCategory C] :
conv_rhs => rw [← category.id_comp f, tensor_comp]
left_unitality' := by tidy
right_unitality' := fun X => by
- ext ⟨f, ⟨⟩⟩; dsimp at f
+ ext ⟨f, ⟨⟩⟩; dsimp at f
dsimp; simp only [category.assoc]
rw [right_unitor_naturality, unitors_inv_equal, iso.inv_hom_id_assoc] }
#align category_theory.coyoneda_tensor_unit CategoryTheory.coyonedaTensorUnit
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Scott Morrison
-/
-import Mathbin.CategoryTheory.Monoidal.Types.Basic
-import Mathbin.CategoryTheory.Monoidal.CoherenceLemmas
+import CategoryTheory.Monoidal.Types.Basic
+import CategoryTheory.Monoidal.CoherenceLemmas
#align_import category_theory.monoidal.types.coyoneda from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.monoidal.types.coyoneda
-! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Monoidal.Types.Basic
import Mathbin.CategoryTheory.Monoidal.CoherenceLemmas
+#align_import category_theory.monoidal.types.coyoneda from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
+
/-!
# `(𝟙_ C ⟶ -)` is a lax monoidal functor to `Type`
mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Scott Morrison
! This file was ported from Lean 3 source module category_theory.monoidal.types.coyoneda
-! leanprover-community/mathlib commit 95a87616d63b3cb49d3fe678d416fbe9c4217bf4
+! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
! 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.Monoidal.CoherenceLemmas
/-!
# `(𝟙_ C ⟶ -)` is a lax monoidal functor to `Type`
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -31,6 +31,7 @@ open Opposite
open MonoidalCategory
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.coyonedaTensorUnit /-
/-- `(𝟙_ C ⟶ -)` is a lax monoidal functor to `Type`. -/
def coyonedaTensorUnit (C : Type u) [Category.{v} C] [MonoidalCategory C] :
LaxMonoidalFunctor C (Type v) :=
@@ -51,6 +52,7 @@ def coyonedaTensorUnit (C : Type u) [Category.{v} C] [MonoidalCategory C] :
dsimp; simp only [category.assoc]
rw [right_unitor_naturality, unitors_inv_equal, iso.inv_hom_id_assoc] }
#align category_theory.coyoneda_tensor_unit CategoryTheory.coyonedaTensorUnit
+-/
end CategoryTheory
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -39,7 +39,7 @@ def coyonedaTensorUnit (C : Type u) [Category.{v} C] [MonoidalCategory C] :
μ := fun X Y p => (λ_ (𝟙_ C)).inv ≫ (p.1 ⊗ p.2)
μ_natural' := by tidy
associativity' := fun X Y Z => by
- ext ⟨⟨f, g⟩, h⟩; dsimp at f g h
+ ext ⟨⟨f, g⟩, h⟩; dsimp at f g h
dsimp; simp only [iso.cancel_iso_inv_left, category.assoc]
conv_lhs =>
rw [← category.id_comp h, tensor_comp, category.assoc, associator_naturality, ←
@@ -47,7 +47,7 @@ def coyonedaTensorUnit (C : Type u) [Category.{v} C] [MonoidalCategory C] :
conv_rhs => rw [← category.id_comp f, tensor_comp]
left_unitality' := by tidy
right_unitality' := fun X => by
- ext ⟨f, ⟨⟩⟩; dsimp at f
+ ext ⟨f, ⟨⟩⟩; dsimp at f
dsimp; simp only [category.assoc]
rw [right_unitor_naturality, unitors_inv_equal, iso.inv_hom_id_assoc] }
#align category_theory.coyoneda_tensor_unit CategoryTheory.coyonedaTensorUnit
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
@@ -33,8 +33,6 @@ open MonoidalCategory
-- I don't know if that is a problem, might need to change it back in the future, but
-- if so it might be better to fix then instead of at the moment of porting.
-attribute [local simp] id_tensorHom tensorHom_id
-
/-- `(𝟙_ C ⟶ -)` is a lax monoidal functor to `Type`. -/
noncomputable
def coyonedaTensorUnit (C : Type u) [Category.{v} C] [MonoidalCategory C] :
@@ -48,13 +46,18 @@ def coyonedaTensorUnit (C : Type u) [Category.{v} C] [MonoidalCategory C] :
dsimp; simp only [Iso.cancel_iso_inv_left, Category.assoc]
conv_lhs =>
rw [← Category.id_comp h, tensor_comp, Category.assoc, associator_naturality, ←
- Category.assoc, unitors_inv_equal, triangle_assoc_comp_right_inv]
- conv_rhs => rw [← Category.id_comp f, tensor_comp])
- (left_unitality := by aesop_cat)
+ Category.assoc, unitors_inv_equal, tensorHom_id, triangle_assoc_comp_right_inv]
+ conv_rhs => rw [← Category.id_comp f, tensor_comp]
+ simp)
+ (left_unitality := by
+ intros
+ ext ⟨⟨⟩, f⟩; dsimp at f
+ dsimp
+ simp)
(right_unitality := fun X => by
ext ⟨f, ⟨⟩⟩; dsimp at f
- dsimp; simp only [Category.assoc]
- rw [rightUnitor_naturality, unitors_inv_equal, Iso.inv_hom_id_assoc])
+ dsimp
+ simp [unitors_inv_equal])
#align category_theory.coyoneda_tensor_unit CategoryTheory.coyonedaTensorUnit
end CategoryTheory
Extracted from #6307. The main reason why #6307 is so large is that many tensoring of identity morphisms that appear in mathlib should be replaced with whiskerings. This PR will leave this issue and deal with other parts. That is, we do not set id_tensorHom
and tensorHom_id
as simple lemmas at this moment, We can set them as simp lemmas locally to enable simple normal forms.
@@ -33,6 +33,8 @@ open MonoidalCategory
-- I don't know if that is a problem, might need to change it back in the future, but
-- if so it might be better to fix then instead of at the moment of porting.
+attribute [local simp] id_tensorHom tensorHom_id
+
/-- `(𝟙_ C ⟶ -)` is a lax monoidal functor to `Type`. -/
noncomputable
def coyonedaTensorUnit (C : Type u) [Category.{v} C] [MonoidalCategory C] :
@@ -36,23 +36,23 @@ open MonoidalCategory
/-- `(𝟙_ C ⟶ -)` is a lax monoidal functor to `Type`. -/
noncomputable
def coyonedaTensorUnit (C : Type u) [Category.{v} C] [MonoidalCategory C] :
- LaxMonoidalFunctor C (Type v) :=
- { coyoneda.obj (op (𝟙_ C)) with
- ε := fun _p => 𝟙 _
- μ := fun X Y p => (λ_ (𝟙_ C)).inv ≫ (p.1 ⊗ p.2)
- μ_natural := by aesop_cat
- associativity := fun X Y Z => by
+ LaxMonoidalFunctor C (Type v) := .ofTensorHom
+ (F := coyoneda.obj (op (𝟙_ C)))
+ (ε := fun _p => 𝟙 _)
+ (μ := fun X Y p => (λ_ (𝟙_ C)).inv ≫ (p.1 ⊗ p.2))
+ (μ_natural := by aesop_cat)
+ (associativity := fun X Y Z => by
ext ⟨⟨f, g⟩, h⟩; dsimp at f g h
dsimp; simp only [Iso.cancel_iso_inv_left, Category.assoc]
conv_lhs =>
rw [← Category.id_comp h, tensor_comp, Category.assoc, associator_naturality, ←
Category.assoc, unitors_inv_equal, triangle_assoc_comp_right_inv]
- conv_rhs => rw [← Category.id_comp f, tensor_comp]
- left_unitality := by aesop_cat
- right_unitality := fun X => by
+ conv_rhs => rw [← Category.id_comp f, tensor_comp])
+ (left_unitality := by aesop_cat)
+ (right_unitality := fun X => by
ext ⟨f, ⟨⟩⟩; dsimp at f
dsimp; simp only [Category.assoc]
- rw [rightUnitor_naturality, unitors_inv_equal, Iso.inv_hom_id_assoc] }
+ rw [rightUnitor_naturality, unitors_inv_equal, Iso.inv_hom_id_assoc])
#align category_theory.coyoneda_tensor_unit CategoryTheory.coyonedaTensorUnit
end CategoryTheory
@@ -2,15 +2,12 @@
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.monoidal.types.coyoneda
-! leanprover-community/mathlib commit 95a87616d63b3cb49d3fe678d416fbe9c4217bf4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Monoidal.Types.Basic
import Mathlib.CategoryTheory.Monoidal.CoherenceLemmas
+#align_import category_theory.monoidal.types.coyoneda from "leanprover-community/mathlib"@"95a87616d63b3cb49d3fe678d416fbe9c4217bf4"
+
/-!
# `(𝟙_ C ⟶ -)` is a lax monoidal functor to `Type`
-/
The unported dependencies are