category_theory.monoidal.coherence_lemmas
⟷
Mathlib.CategoryTheory.Monoidal.CoherenceLemmas
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
@@ -3,7 +3,7 @@ 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, Bhavik Mehta, Jakob von Raumer
-/
-import CategoryTheory.Monoidal.Coherence
+import Tactic.CategoryTheory.Coherence
#align_import category_theory.monoidal.coherence_lemmas from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -43,20 +43,20 @@ theorem leftUnitor_tensor'' (X Y : C) : (α_ (𝟙_ C) X Y).Hom ≫ (λ_ (X ⊗
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print CategoryTheory.MonoidalCategory.leftUnitor_tensor /-
+#print CategoryTheory.MonoidalCategory.leftUnitor_tensor' /-
@[reassoc, simp]
-theorem leftUnitor_tensor (X Y : C) : (λ_ (X ⊗ Y)).Hom = (α_ (𝟙_ C) X Y).inv ≫ ((λ_ X).Hom ⊗ 𝟙 Y) :=
- by coherence
-#align category_theory.monoidal_category.left_unitor_tensor CategoryTheory.MonoidalCategory.leftUnitor_tensor
+theorem leftUnitor_tensor' (X Y : C) :
+ (λ_ (X ⊗ Y)).Hom = (α_ (𝟙_ C) X Y).inv ≫ ((λ_ X).Hom ⊗ 𝟙 Y) := by coherence
+#align category_theory.monoidal_category.left_unitor_tensor CategoryTheory.MonoidalCategory.leftUnitor_tensor'
-/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv /-
+#print CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv' /-
@[reassoc]
-theorem leftUnitor_tensor_inv (X Y : C) :
+theorem leftUnitor_tensor_inv' (X Y : C) :
(λ_ (X ⊗ Y)).inv = ((λ_ X).inv ⊗ 𝟙 Y) ≫ (α_ (𝟙_ C) X Y).Hom := by coherence
-#align category_theory.monoidal_category.left_unitor_tensor_inv CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv
+#align category_theory.monoidal_category.left_unitor_tensor_inv CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv'
-/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -33,12 +33,12 @@ variable {C : Type _} [Category C] [MonoidalCategory C]
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print CategoryTheory.MonoidalCategory.leftUnitor_tensor' /-
+#print CategoryTheory.MonoidalCategory.leftUnitor_tensor'' /-
-- See Proposition 2.2.4 of <http://www-math.mit.edu/~etingof/egnobookfinal.pdf>
@[reassoc]
-theorem leftUnitor_tensor' (X Y : C) : (α_ (𝟙_ C) X Y).Hom ≫ (λ_ (X ⊗ Y)).Hom = (λ_ X).Hom ⊗ 𝟙 Y :=
+theorem leftUnitor_tensor'' (X Y : C) : (α_ (𝟙_ C) X Y).Hom ≫ (λ_ (X ⊗ Y)).Hom = (λ_ X).Hom ⊗ 𝟙 Y :=
by coherence
-#align category_theory.monoidal_category.left_unitor_tensor' CategoryTheory.MonoidalCategory.leftUnitor_tensor'
+#align category_theory.monoidal_category.left_unitor_tensor' CategoryTheory.MonoidalCategory.leftUnitor_tensor''
-/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ 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, Bhavik Mehta, Jakob von Raumer
-/
-import Mathbin.CategoryTheory.Monoidal.Coherence
+import CategoryTheory.Monoidal.Coherence
#align_import category_theory.monoidal.coherence_lemmas from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
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, Bhavik Mehta, Jakob von Raumer
-
-! This file was ported from Lean 3 source module category_theory.monoidal.coherence_lemmas
-! leanprover-community/mathlib commit f60c6087a7275b72d5db3c5a1d0e19e35a429c0a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Monoidal.Coherence
+#align_import category_theory.monoidal.coherence_lemmas from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
+
/-!
# Lemmas which are consequences of monoidal coherence
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Scott Morrison, Bhavik Mehta, Jakob von Raumer
! This file was ported from Lean 3 source module category_theory.monoidal.coherence_lemmas
-! leanprover-community/mathlib commit b8b8bf3ea0c625fa1f950034a184e07c67f7bcfe
+! leanprover-community/mathlib commit f60c6087a7275b72d5db3c5a1d0e19e35a429c0a
! 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.Coherence
/-!
# Lemmas which are consequences of monoidal coherence
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
These lemmas are all proved `by coherence`.
## Future work
@@ -33,86 +36,108 @@ variable {C : Type _} [Category C] [MonoidalCategory C]
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.MonoidalCategory.leftUnitor_tensor' /-
-- See Proposition 2.2.4 of <http://www-math.mit.edu/~etingof/egnobookfinal.pdf>
@[reassoc]
theorem leftUnitor_tensor' (X Y : C) : (α_ (𝟙_ C) X Y).Hom ≫ (λ_ (X ⊗ Y)).Hom = (λ_ X).Hom ⊗ 𝟙 Y :=
by coherence
#align category_theory.monoidal_category.left_unitor_tensor' CategoryTheory.MonoidalCategory.leftUnitor_tensor'
+-/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.MonoidalCategory.leftUnitor_tensor /-
@[reassoc, simp]
theorem leftUnitor_tensor (X Y : C) : (λ_ (X ⊗ Y)).Hom = (α_ (𝟙_ C) X Y).inv ≫ ((λ_ X).Hom ⊗ 𝟙 Y) :=
by coherence
#align category_theory.monoidal_category.left_unitor_tensor CategoryTheory.MonoidalCategory.leftUnitor_tensor
+-/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv /-
@[reassoc]
theorem leftUnitor_tensor_inv (X Y : C) :
(λ_ (X ⊗ Y)).inv = ((λ_ X).inv ⊗ 𝟙 Y) ≫ (α_ (𝟙_ C) X Y).Hom := by coherence
#align category_theory.monoidal_category.left_unitor_tensor_inv CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv
+-/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv /-
@[reassoc]
theorem id_tensor_rightUnitor_inv (X Y : C) : 𝟙 X ⊗ (ρ_ Y).inv = (ρ_ _).inv ≫ (α_ _ _ _).Hom := by
coherence
#align category_theory.monoidal_category.id_tensor_right_unitor_inv CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv
+-/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.MonoidalCategory.leftUnitor_inv_tensor_id /-
@[reassoc]
theorem leftUnitor_inv_tensor_id (X Y : C) : (λ_ X).inv ⊗ 𝟙 Y = (λ_ _).inv ≫ (α_ _ _ _).inv := by
coherence
#align category_theory.monoidal_category.left_unitor_inv_tensor_id CategoryTheory.MonoidalCategory.leftUnitor_inv_tensor_id
+-/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom /-
@[reassoc]
theorem pentagon_inv_inv_hom (W X Y Z : C) :
(α_ W (X ⊗ Y) Z).inv ≫ ((α_ W X Y).inv ⊗ 𝟙 Z) ≫ (α_ (W ⊗ X) Y Z).Hom =
(𝟙 W ⊗ (α_ X Y Z).Hom) ≫ (α_ W X (Y ⊗ Z)).inv :=
by coherence
#align category_theory.monoidal_category.pentagon_inv_inv_hom CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom
+-/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv /-
@[simp, reassoc]
theorem triangle_assoc_comp_right_inv (X Y : C) :
((ρ_ X).inv ⊗ 𝟙 Y) ≫ (α_ X (𝟙_ C) Y).Hom = 𝟙 X ⊗ (λ_ Y).inv := by coherence
#align category_theory.monoidal_category.triangle_assoc_comp_right_inv CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv
+-/
+#print CategoryTheory.MonoidalCategory.unitors_equal /-
theorem unitors_equal : (λ_ (𝟙_ C)).Hom = (ρ_ (𝟙_ C)).Hom := by coherence
#align category_theory.monoidal_category.unitors_equal CategoryTheory.MonoidalCategory.unitors_equal
+-/
+#print CategoryTheory.MonoidalCategory.unitors_inv_equal /-
theorem unitors_inv_equal : (λ_ (𝟙_ C)).inv = (ρ_ (𝟙_ C)).inv := by coherence
#align category_theory.monoidal_category.unitors_inv_equal CategoryTheory.MonoidalCategory.unitors_inv_equal
+-/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.MonoidalCategory.pentagon_hom_inv /-
@[reassoc]
theorem pentagon_hom_inv {W X Y Z : C} :
(α_ W X (Y ⊗ Z)).Hom ≫ (𝟙 W ⊗ (α_ X Y Z).inv) =
(α_ (W ⊗ X) Y Z).inv ≫ ((α_ W X Y).Hom ⊗ 𝟙 Z) ≫ (α_ W (X ⊗ Y) Z).Hom :=
by coherence
#align category_theory.monoidal_category.pentagon_hom_inv CategoryTheory.MonoidalCategory.pentagon_hom_inv
+-/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.MonoidalCategory.pentagon_inv_hom /-
@[reassoc]
theorem pentagon_inv_hom (W X Y Z : C) :
(α_ (W ⊗ X) Y Z).inv ≫ ((α_ W X Y).Hom ⊗ 𝟙 Z) =
(α_ W X (Y ⊗ Z)).Hom ≫ (𝟙 W ⊗ (α_ X Y Z).inv) ≫ (α_ W (X ⊗ Y) Z).inv :=
by coherence
#align category_theory.monoidal_category.pentagon_inv_hom CategoryTheory.MonoidalCategory.pentagon_inv_hom
+-/
end CategoryTheory.MonoidalCategory
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -34,33 +34,33 @@ variable {C : Type _} [Category C] [MonoidalCategory C]
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-- See Proposition 2.2.4 of <http://www-math.mit.edu/~etingof/egnobookfinal.pdf>
-@[reassoc.1]
+@[reassoc]
theorem leftUnitor_tensor' (X Y : C) : (α_ (𝟙_ C) X Y).Hom ≫ (λ_ (X ⊗ Y)).Hom = (λ_ X).Hom ⊗ 𝟙 Y :=
by coherence
#align category_theory.monoidal_category.left_unitor_tensor' CategoryTheory.MonoidalCategory.leftUnitor_tensor'
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-@[reassoc.1, simp]
+@[reassoc, simp]
theorem leftUnitor_tensor (X Y : C) : (λ_ (X ⊗ Y)).Hom = (α_ (𝟙_ C) X Y).inv ≫ ((λ_ X).Hom ⊗ 𝟙 Y) :=
by coherence
#align category_theory.monoidal_category.left_unitor_tensor CategoryTheory.MonoidalCategory.leftUnitor_tensor
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-@[reassoc.1]
+@[reassoc]
theorem leftUnitor_tensor_inv (X Y : C) :
(λ_ (X ⊗ Y)).inv = ((λ_ X).inv ⊗ 𝟙 Y) ≫ (α_ (𝟙_ C) X Y).Hom := by coherence
#align category_theory.monoidal_category.left_unitor_tensor_inv CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-@[reassoc.1]
+@[reassoc]
theorem id_tensor_rightUnitor_inv (X Y : C) : 𝟙 X ⊗ (ρ_ Y).inv = (ρ_ _).inv ≫ (α_ _ _ _).Hom := by
coherence
#align category_theory.monoidal_category.id_tensor_right_unitor_inv CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-@[reassoc.1]
+@[reassoc]
theorem leftUnitor_inv_tensor_id (X Y : C) : (λ_ X).inv ⊗ 𝟙 Y = (λ_ _).inv ≫ (α_ _ _ _).inv := by
coherence
#align category_theory.monoidal_category.left_unitor_inv_tensor_id CategoryTheory.MonoidalCategory.leftUnitor_inv_tensor_id
@@ -70,7 +70,7 @@ theorem leftUnitor_inv_tensor_id (X Y : C) : (λ_ X).inv ⊗ 𝟙 Y = (λ_ _).in
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-@[reassoc.1]
+@[reassoc]
theorem pentagon_inv_inv_hom (W X Y Z : C) :
(α_ W (X ⊗ Y) Z).inv ≫ ((α_ W X Y).inv ⊗ 𝟙 Z) ≫ (α_ (W ⊗ X) Y Z).Hom =
(𝟙 W ⊗ (α_ X Y Z).Hom) ≫ (α_ W X (Y ⊗ Z)).inv :=
@@ -79,7 +79,7 @@ theorem pentagon_inv_inv_hom (W X Y Z : C) :
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-@[simp, reassoc.1]
+@[simp, reassoc]
theorem triangle_assoc_comp_right_inv (X Y : C) :
((ρ_ X).inv ⊗ 𝟙 Y) ≫ (α_ X (𝟙_ C) Y).Hom = 𝟙 X ⊗ (λ_ Y).inv := by coherence
#align category_theory.monoidal_category.triangle_assoc_comp_right_inv CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv
@@ -95,7 +95,7 @@ theorem unitors_inv_equal : (λ_ (𝟙_ C)).inv = (ρ_ (𝟙_ C)).inv := by cohe
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-@[reassoc.1]
+@[reassoc]
theorem pentagon_hom_inv {W X Y Z : C} :
(α_ W X (Y ⊗ Z)).Hom ≫ (𝟙 W ⊗ (α_ X Y Z).inv) =
(α_ (W ⊗ X) Y Z).inv ≫ ((α_ W X Y).Hom ⊗ 𝟙 Z) ≫ (α_ W (X ⊗ Y) Z).Hom :=
@@ -107,7 +107,7 @@ theorem pentagon_hom_inv {W X Y Z : C} :
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-@[reassoc.1]
+@[reassoc]
theorem pentagon_inv_hom (W X Y Z : C) :
(α_ (W ⊗ X) Y Z).inv ≫ ((α_ W X Y).Hom ⊗ 𝟙 Z) =
(α_ W X (Y ⊗ Z)).Hom ≫ (𝟙 W ⊗ (α_ X Y Z).inv) ≫ (α_ W (X ⊗ Y) Z).inv :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -33,15 +33,15 @@ theorem leftUnitor_tensor'' (X Y : C) :
#align category_theory.monoidal_category.left_unitor_tensor' CategoryTheory.MonoidalCategory.leftUnitor_tensor''
@[reassoc]
-theorem leftUnitor_tensor (X Y : C) :
+theorem leftUnitor_tensor' (X Y : C) :
(λ_ (X ⊗ Y)).hom = (α_ (𝟙_ C) X Y).inv ≫ ((λ_ X).hom ⊗ 𝟙 Y) := by
coherence
-#align category_theory.monoidal_category.left_unitor_tensor CategoryTheory.MonoidalCategory.leftUnitor_tensor
+#align category_theory.monoidal_category.left_unitor_tensor CategoryTheory.MonoidalCategory.leftUnitor_tensor'
@[reassoc]
-theorem leftUnitor_tensor_inv (X Y : C) :
+theorem leftUnitor_tensor_inv' (X Y : C) :
(λ_ (X ⊗ Y)).inv = ((λ_ X).inv ⊗ 𝟙 Y) ≫ (α_ (𝟙_ C) X Y).hom := by coherence
-#align category_theory.monoidal_category.left_unitor_tensor_inv CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv
+#align category_theory.monoidal_category.left_unitor_tensor_inv CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv'
@[reassoc]
theorem id_tensor_rightUnitor_inv (X Y : C) : 𝟙 X ⊗ (ρ_ Y).inv = (ρ_ _).inv ≫ (α_ _ _ _).hom := by
@@ -60,12 +60,6 @@ theorem pentagon_inv_inv_hom (W X Y Z : C) :
coherence
#align category_theory.monoidal_category.pentagon_inv_inv_hom CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom
-@[reassoc (attr := simp)]
-theorem triangle_assoc_comp_right_inv (X Y : C) :
- ((ρ_ X).inv ⊗ 𝟙 Y) ≫ (α_ X (𝟙_ C) Y).hom = 𝟙 X ⊗ (λ_ Y).inv := by
- coherence
-#align category_theory.monoidal_category.triangle_assoc_comp_right_inv CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv
-
theorem unitors_equal : (λ_ (𝟙_ C)).hom = (ρ_ (𝟙_ C)).hom := by
coherence
#align category_theory.monoidal_category.unitors_equal CategoryTheory.MonoidalCategory.unitors_equal
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.
@@ -27,12 +27,12 @@ variable {C : Type*} [Category C] [MonoidalCategory C]
-- See Proposition 2.2.4 of <http://www-math.mit.edu/~etingof/egnobookfinal.pdf>
@[reassoc]
-theorem leftUnitor_tensor' (X Y : C) :
+theorem leftUnitor_tensor'' (X Y : C) :
(α_ (𝟙_ C) X Y).hom ≫ (λ_ (X ⊗ Y)).hom = (λ_ X).hom ⊗ 𝟙 Y := by
coherence
-#align category_theory.monoidal_category.left_unitor_tensor' CategoryTheory.MonoidalCategory.leftUnitor_tensor'
+#align category_theory.monoidal_category.left_unitor_tensor' CategoryTheory.MonoidalCategory.leftUnitor_tensor''
-@[reassoc, simp]
+@[reassoc]
theorem leftUnitor_tensor (X Y : C) :
(λ_ (X ⊗ Y)).hom = (α_ (𝟙_ C) X Y).inv ≫ ((λ_ X).hom ⊗ 𝟙 Y) := by
coherence
@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Scott Morrison, Bhavik Mehta, Jakob von Raumer
-/
import Mathlib.Tactic.CategoryTheory.Coherence
+import Mathlib.CategoryTheory.Monoidal.Free.Coherence
#align_import category_theory.monoidal.coherence_lemmas from "leanprover-community/mathlib"@"b8b8bf3ea0c625fa1f950034a184e07c67f7bcfe"
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -22,7 +22,7 @@ open CategoryTheory Category Iso
namespace CategoryTheory.MonoidalCategory
-variable {C : Type _} [Category C] [MonoidalCategory C]
+variable {C : Type*} [Category C] [MonoidalCategory C]
-- See Proposition 2.2.4 of <http://www-math.mit.edu/~etingof/egnobookfinal.pdf>
@[reassoc]
@@ -2,14 +2,11 @@
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, Bhavik Mehta, Jakob von Raumer
-
-! This file was ported from Lean 3 source module category_theory.monoidal.coherence_lemmas
-! leanprover-community/mathlib commit b8b8bf3ea0c625fa1f950034a184e07c67f7bcfe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Tactic.CategoryTheory.Coherence
+#align_import category_theory.monoidal.coherence_lemmas from "leanprover-community/mathlib"@"b8b8bf3ea0c625fa1f950034a184e07c67f7bcfe"
+
/-!
# Lemmas which are consequences of monoidal coherence
All dependencies are ported!