category_theory.monoidal.coherence | Mathlib porting status

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Yuma Mizuno, Oleksandr Manzyuk
 -/
 import CategoryTheory.Monoidal.Free.Coherence
-import CategoryTheory.Bicategory.CoherenceTactic
+import Tactic.CategoryTheory.BicategoryCoherence
 
 #align_import category_theory.monoidal.coherence from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"

bump to nightly-2024-02-05-08

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

516c6ec2

Diff

@@ -102,7 +102,7 @@ instance liftHomTensor {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y] [LiftOb
     where lift := LiftHom.lift f ⊗ LiftHom.lift g
 #align category_theory.monoidal_category.lift_hom_tensor CategoryTheory.MonoidalCategory.liftHomTensor
 
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`Hom] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`Hom] [] -/
 -- We could likely turn this into a `Prop` valued existential if that proves useful.
 /-- A typeclass carrying a choice of monoidal structural isomorphism between two objects.
 Used by the `⊗≫` monoidal composition operator, and the `coherence` tactic.

bump to nightly-2023-12-23-06

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

b8c74971

Diff

@@ -102,7 +102,7 @@ instance liftHomTensor {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y] [LiftOb
     where lift := LiftHom.lift f ⊗ LiftHom.lift g
 #align category_theory.monoidal_category.lift_hom_tensor CategoryTheory.MonoidalCategory.liftHomTensor
 
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`Hom] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`Hom] [] -/
 -- We could likely turn this into a `Prop` valued existential if that proves useful.
 /-- A typeclass carrying a choice of monoidal structural isomorphism between two objects.
 Used by the `⊗≫` monoidal composition operator, and the `coherence` tactic.

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2022. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Yuma Mizuno, Oleksandr Manzyuk
 -/
-import Mathbin.CategoryTheory.Monoidal.Free.Coherence
-import Mathbin.CategoryTheory.Bicategory.CoherenceTactic
+import CategoryTheory.Monoidal.Free.Coherence
+import CategoryTheory.Bicategory.CoherenceTactic
 
 #align_import category_theory.monoidal.coherence from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
 
@@ -102,7 +102,7 @@ instance liftHomTensor {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y] [LiftOb
     where lift := LiftHom.lift f ⊗ LiftHom.lift g
 #align category_theory.monoidal_category.lift_hom_tensor CategoryTheory.MonoidalCategory.liftHomTensor
 
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`Hom] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`Hom] [] -/
 -- We could likely turn this into a `Prop` valued existential if that proves useful.
 /-- A typeclass carrying a choice of monoidal structural isomorphism between two objects.
 Used by the `⊗≫` monoidal composition operator, and the `coherence` tactic.
@@ -300,7 +300,7 @@ unsafe def mk_project_map_expr (e : expr) : tactic expr :=
         (CategoryTheory.MonoidalCategory.LiftHom.lift $(e)))
 #align tactic.mk_project_map_expr tactic.mk_project_map_expr
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
 -- PLEASE REPORT THIS TO MATHPORT DEVS, THIS SHOULD NOT HAPPEN.
 -- failed to format: unknown constant 'term.pseudo.antiquot'
 /-- Coherence tactic for monoidal categories. -/ unsafe
@@ -365,9 +365,9 @@ theorem assoc_liftHom {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y] (f : W 
   (Category.assoc _ _ _).symm
 #align tactic.coherence.assoc_lift_hom Tactic.Coherence.assoc_liftHom
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
 /-- Internal tactic used in `coherence`.
 
 Rewrites an equation `f = g` as `f₀ ≫ f₁ = g₀ ≫ g₁`,
@@ -400,8 +400,8 @@ end Coherence
 
 open Coherence
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
 /-- The main part of `coherence` tactic. -/
 unsafe def coherence_loop : tactic Unit := do
   -- To prove an equality `f = g` in a monoidal category,
@@ -443,8 +443,8 @@ unsafe def coherence_loop : tactic Unit := do
             coherence_loop
 #align tactic.coherence_loop tactic.coherence_loop
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
 /-- Use the coherence theorem for monoidal categories to solve equations in a monoidal equation,
 where the two sides only differ by replacing strings of monoidal structural morphisms
 (that is, associators, unitors, and identities)

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Yuma Mizuno, Oleksandr Manzyuk
-
-! This file was ported from Lean 3 source module category_theory.monoidal.coherence
-! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Monoidal.Free.Coherence
 import Mathbin.CategoryTheory.Bicategory.CoherenceTactic
 
+#align_import category_theory.monoidal.coherence from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
+
 /-!
 # A `coherence` tactic for monoidal categories, and `⊗≫` (composition up to associators)

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -105,7 +105,7 @@ instance liftHomTensor {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y] [LiftOb
     where lift := LiftHom.lift f ⊗ LiftHom.lift g
 #align category_theory.monoidal_category.lift_hom_tensor CategoryTheory.MonoidalCategory.liftHomTensor
 
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`Hom] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`Hom] [] -/
 -- We could likely turn this into a `Prop` valued existential if that proves useful.
 /-- A typeclass carrying a choice of monoidal structural isomorphism between two objects.
 Used by the `⊗≫` monoidal composition operator, and the `coherence` tactic.
@@ -244,7 +244,6 @@ def monoidalComp {W X Y Z : C} [LiftObj X] [LiftObj Y] [MonoidalCoherence X Y] (
   f ≫ MonoidalCoherence.hom X Y ≫ g
 #align category_theory.monoidal_category.monoidal_comp CategoryTheory.MonoidalCategory.monoidalComp
 
--- mathport name: «expr ⊗≫ »
 infixr:80 " ⊗≫ " => monoidalComp
 
 -- type as \ot \gg
@@ -255,7 +254,6 @@ def monoidalIsoComp {W X Y Z : C} [LiftObj X] [LiftObj Y] [MonoidalCoherence X Y
   f ≪≫ asIso (MonoidalCoherence.hom X Y) ≪≫ g
 #align category_theory.monoidal_category.monoidal_iso_comp CategoryTheory.MonoidalCategory.monoidalIsoComp
 
--- mathport name: «expr ≪⊗≫ »
 infixr:80 " ≪⊗≫ " => monoidalIsoComp
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -305,7 +305,7 @@ unsafe def mk_project_map_expr (e : expr) : tactic expr :=
         (CategoryTheory.MonoidalCategory.LiftHom.lift $(e)))
 #align tactic.mk_project_map_expr tactic.mk_project_map_expr
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
 -- PLEASE REPORT THIS TO MATHPORT DEVS, THIS SHOULD NOT HAPPEN.
 -- failed to format: unknown constant 'term.pseudo.antiquot'
 /-- Coherence tactic for monoidal categories. -/ unsafe
@@ -370,9 +370,9 @@ theorem assoc_liftHom {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y] (f : W 
   (Category.assoc _ _ _).symm
 #align tactic.coherence.assoc_lift_hom Tactic.Coherence.assoc_liftHom
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
 /-- Internal tactic used in `coherence`.
 
 Rewrites an equation `f = g` as `f₀ ≫ f₁ = g₀ ≫ g₁`,
@@ -405,8 +405,8 @@ end Coherence
 
 open Coherence
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
 /-- The main part of `coherence` tactic. -/
 unsafe def coherence_loop : tactic Unit := do
   -- To prove an equality `f = g` in a monoidal category,
@@ -448,8 +448,8 @@ unsafe def coherence_loop : tactic Unit := do
             coherence_loop
 #align tactic.coherence_loop tactic.coherence_loop
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
 /-- Use the coherence theorem for monoidal categories to solve equations in a monoidal equation,
 where the two sides only differ by replacing strings of monoidal structural morphisms
 (that is, associators, unitors, and identities)

bump to nightly-2023-06-09-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

fe176e9b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Yuma Mizuno, Oleksandr Manzyuk
 
 ! This file was ported from Lean 3 source module category_theory.monoidal.coherence
-! leanprover-community/mathlib commit 4d0b6301ef962e6bd74462998943ce38b7adb132
+! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.CategoryTheory.Bicategory.CoherenceTactic
 /-!
 # A `coherence` tactic for monoidal categories, and `⊗≫` (composition up to associators)
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We provide a `coherence` tactic,
 which proves equations where the two sides differ by replacing
 strings of monoidal structural morphisms with other such strings.

bump to nightly-2023-06-08-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

d3cfe2e3

Diff

@@ -303,6 +303,7 @@ unsafe def mk_project_map_expr (e : expr) : tactic expr :=
 #align tactic.mk_project_map_expr tactic.mk_project_map_expr
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+-- PLEASE REPORT THIS TO MATHPORT DEVS, THIS SHOULD NOT HAPPEN.
 -- failed to format: unknown constant 'term.pseudo.antiquot'
 /-- Coherence tactic for monoidal categories. -/ unsafe
   def

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -102,7 +102,7 @@ instance liftHomTensor {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y] [LiftOb
     where lift := LiftHom.lift f ⊗ LiftHom.lift g
 #align category_theory.monoidal_category.lift_hom_tensor CategoryTheory.MonoidalCategory.liftHomTensor
 
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`Hom] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`Hom] [] -/
 -- We could likely turn this into a `Prop` valued existential if that proves useful.
 /-- A typeclass carrying a choice of monoidal structural isomorphism between two objects.
 Used by the `⊗≫` monoidal composition operator, and the `coherence` tactic.

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -273,10 +273,8 @@ example {W X Y Z : C} (f : W ⟶ (X ⊗ Y) ⊗ Z) : W ⟶ X ⊗ Y ⊗ Z :=
   f ⊗≫ 𝟙 _
 
 @[simp]
-theorem monoidalComp_refl {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z) : f ⊗≫ g = f ≫ g :=
-  by
-  dsimp [monoidal_comp]
-  simp
+theorem monoidalComp_refl {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z) : f ⊗≫ g = f ≫ g := by
+  dsimp [monoidal_comp]; simp
 #align category_theory.monoidal_category.monoidal_comp_refl CategoryTheory.MonoidalCategory.monoidalComp_refl
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/

bump to nightly-2023-04-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

ff662d55

Diff

@@ -102,7 +102,7 @@ instance liftHomTensor {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y] [LiftOb
     where lift := LiftHom.lift f ⊗ LiftHom.lift g
 #align category_theory.monoidal_category.lift_hom_tensor CategoryTheory.MonoidalCategory.liftHomTensor
 
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`Hom] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`Hom] [] -/
 -- We could likely turn this into a `Prop` valued existential if that proves useful.
 /-- A typeclass carrying a choice of monoidal structural isomorphism between two objects.
 Used by the `⊗≫` monoidal composition operator, and the `coherence` tactic.

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -304,7 +304,7 @@ unsafe def mk_project_map_expr (e : expr) : tactic expr :=
         (CategoryTheory.MonoidalCategory.LiftHom.lift $(e)))
 #align tactic.mk_project_map_expr tactic.mk_project_map_expr
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
 -- failed to format: unknown constant 'term.pseudo.antiquot'
 /-- Coherence tactic for monoidal categories. -/ unsafe
   def
@@ -338,7 +338,7 @@ unsafe def pure_coherence : tactic Unit :=
   monoidal_coherence <|> bicategorical_coherence
 #align tactic.pure_coherence tactic.pure_coherence
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic tactic.pure_coherence -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic tactic.pure_coherence -/
 /- ./././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 -/
@@ -368,9 +368,9 @@ theorem assoc_liftHom {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y] (f : W 
   (Category.assoc _ _ _).symm
 #align tactic.coherence.assoc_lift_hom Tactic.Coherence.assoc_liftHom
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
 /-- Internal tactic used in `coherence`.
 
 Rewrites an equation `f = g` as `f₀ ≫ f₁ = g₀ ≫ g₁`,
@@ -383,7 +383,7 @@ unsafe def liftable_prefixes : tactic Unit := do
   (try sorry >> sorry) >> try sorry
 #align tactic.coherence.liftable_prefixes tactic.coherence.liftable_prefixes
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic tactic.coherence.liftable_prefixes -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic tactic.coherence.liftable_prefixes -/
 example {W X Y Z : C} (f : Y ⟶ Z) (g) (w : False) : (λ_ _).Hom ≫ f = g :=
   by
   run_tac
@@ -403,8 +403,8 @@ end Coherence
 
 open Coherence
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
 /-- The main part of `coherence` tactic. -/
 unsafe def coherence_loop : tactic Unit := do
   -- To prove an equality `f = g` in a monoidal category,
@@ -446,8 +446,8 @@ unsafe def coherence_loop : tactic Unit := do
             coherence_loop
 #align tactic.coherence_loop tactic.coherence_loop
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
 /-- Use the coherence theorem for monoidal categories to solve equations in a monoidal equation,
 where the two sides only differ by replacing strings of monoidal structural morphisms
 (that is, associators, unitors, and identities)

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore(CategoryTheory/Monoidal): replace 𝟙 X ⊗ f with X ◁ f (#11223)

Extracted from #6307

ee3a8f2c

Diff

@@ -262,7 +262,8 @@ elab_rules : tactic
       MonoidalCategory.whiskerRight_tensor, MonoidalCategory.whiskerRight_id,
       MonoidalCategory.whiskerLeft_comp, MonoidalCategory.whiskerLeft_id,
       MonoidalCategory.comp_whiskerRight, MonoidalCategory.id_whiskerRight,
-      MonoidalCategory.whisker_assoc];
+      MonoidalCategory.whisker_assoc,
+      MonoidalCategory.id_tensorHom, MonoidalCategory.tensorHom_id];
     -- I'm not sure if `tensorHom` should be expanded.
     try simp only [MonoidalCategory.tensorHom_def]
     ))

chore(CategoryTheory/MonoidalCategory): split the monoidal composition (#11149)

I realized that the monoid composition ⊗≫ can be defined without depending on the free monoid category, and that it is still useful.

35909eaa

Diff

@@ -6,11 +6,12 @@ Authors: Scott Morrison, Yuma Mizuno, Oleksandr Manzyuk
 import Mathlib.CategoryTheory.Monoidal.Free.Basic
 import Mathlib.Lean.Meta
 import Mathlib.Tactic.CategoryTheory.BicategoryCoherence
+import Mathlib.Tactic.CategoryTheory.MonoidalComp
 
 #align_import category_theory.monoidal.coherence from "leanprover-community/mathlib"@"f187f1074fa1857c94589cc653c786cadc4c35ff"
 
 /-!
-# A `coherence` tactic for monoidal categories, and `⊗≫` (composition up to associators)
+# A `coherence` tactic for monoidal categories
 
 We provide a `coherence` tactic,
 which proves equations where the two sides differ by replacing
@@ -22,9 +23,6 @@ which proves that any two morphisms (with the same source and target)
 in a monoidal category which are built out of associators and unitors
 are equal.
 
-We also provide `f ⊗≫ g`, the `monoidal_comp` operation,
-which automatically inserts associators and unitors as needed
-to make the target of `f` match the source of `g`.
 -/
 
 set_option autoImplicit true
@@ -100,124 +98,6 @@ instance LiftHom_tensor {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y] [LiftO
     (f : W ⟶ X) (g : Y ⟶ Z) [LiftHom f] [LiftHom g] : LiftHom (f ⊗ g) where
   lift := LiftHom.lift f ⊗ LiftHom.lift g
 
-/--
-A typeclass carrying a choice of monoidal structural isomorphism between two objects.
-Used by the `⊗≫` monoidal composition operator, and the `coherence` tactic.
--/
--- We could likely turn this into a `Prop` valued existential if that proves useful.
-class MonoidalCoherence (X Y : C) [LiftObj X] [LiftObj Y] where
-  hom : X ⟶ Y
-  [isIso : IsIso hom]
-
-attribute [instance] MonoidalCoherence.isIso
-
-namespace MonoidalCoherence
-
-@[simps]
-instance refl (X : C) [LiftObj X] : MonoidalCoherence X X := ⟨𝟙 _⟩
-
-@[simps]
-instance whiskerLeft (X Y Z : C) [LiftObj X] [LiftObj Y] [LiftObj Z] [MonoidalCoherence Y Z] :
-    MonoidalCoherence (X ⊗ Y) (X ⊗ Z) :=
-  ⟨X ◁ MonoidalCoherence.hom⟩
-
-@[simps]
-instance whiskerRight (X Y Z : C) [LiftObj X] [LiftObj Y] [LiftObj Z] [MonoidalCoherence X Y] :
-    MonoidalCoherence (X ⊗ Z) (Y ⊗ Z) :=
-  ⟨MonoidalCoherence.hom ▷ Z⟩
-
-@[simps]
-instance tensor_right (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence (𝟙_ C) Y] :
-    MonoidalCoherence X (X ⊗ Y) :=
-  ⟨(ρ_ X).inv ≫ X ◁  MonoidalCoherence.hom⟩
-
-@[simps]
-instance tensor_right' (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence Y (𝟙_ C)] :
-    MonoidalCoherence (X ⊗ Y) X :=
-  ⟨X ◁ MonoidalCoherence.hom ≫ (ρ_ X).hom⟩
-
-@[simps]
-instance left (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence X Y] :
-    MonoidalCoherence (𝟙_ C ⊗ X) Y :=
-  ⟨(λ_ X).hom ≫ MonoidalCoherence.hom⟩
-
-@[simps]
-instance left' (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence X Y] :
-    MonoidalCoherence X (𝟙_ C ⊗ Y) :=
-  ⟨MonoidalCoherence.hom ≫ (λ_ Y).inv⟩
-
-@[simps]
-instance right (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence X Y] :
-    MonoidalCoherence (X ⊗ 𝟙_ C) Y :=
-  ⟨(ρ_ X).hom ≫ MonoidalCoherence.hom⟩
-
-@[simps]
-instance right' (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence X Y] :
-    MonoidalCoherence X (Y ⊗ 𝟙_ C) :=
-  ⟨MonoidalCoherence.hom ≫ (ρ_ Y).inv⟩
-
-@[simps]
-instance assoc (X Y Z W : C) [LiftObj W] [LiftObj X] [LiftObj Y] [LiftObj Z]
-    [MonoidalCoherence (X ⊗ (Y ⊗ Z)) W] : MonoidalCoherence ((X ⊗ Y) ⊗ Z) W :=
-  ⟨(α_ X Y Z).hom ≫ MonoidalCoherence.hom⟩
-
-@[simps]
-instance assoc' (W X Y Z : C) [LiftObj W] [LiftObj X] [LiftObj Y] [LiftObj Z]
-    [MonoidalCoherence W (X ⊗ (Y ⊗ Z))] : MonoidalCoherence W ((X ⊗ Y) ⊗ Z) :=
-  ⟨MonoidalCoherence.hom ≫ (α_ X Y Z).inv⟩
-
-end MonoidalCoherence
-
-/-- Construct an isomorphism between two objects in a monoidal category
-out of unitors and associators. -/
-def monoidalIso (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence X Y] : X ≅ Y :=
-  asIso MonoidalCoherence.hom
-
-example (X : C) : X ≅ (X ⊗ (𝟙_ C ⊗ 𝟙_ C)) := monoidalIso _ _
-
-example (X1 X2 X3 X4 X5 X6 X7 X8 X9 : C) :
-    (𝟙_ C ⊗ (X1 ⊗ X2 ⊗ ((X3 ⊗ X4) ⊗ X5)) ⊗ X6 ⊗ (X7 ⊗ X8 ⊗ X9)) ≅
-    (X1 ⊗ (X2 ⊗ X3) ⊗ X4 ⊗ (X5 ⊗ (𝟙_ C ⊗ X6) ⊗ X7) ⊗ X8 ⊗ X9) :=
-  monoidalIso _ _
-
-/-- Notation for identities up to unitors and associators. -/
-scoped[CategoryTheory.MonoidalCategory] notation " ⊗𝟙 " =>
-  Mathlib.Tactic.Coherence.MonoidalCoherence.hom -- type as \ot 𝟙
-
-/-- Compose two morphisms in a monoidal category,
-inserting unitors and associators between as necessary. -/
-def monoidalComp {W X Y Z : C} [LiftObj X] [LiftObj Y]
-    [MonoidalCoherence X Y] (f : W ⟶ X) (g : Y ⟶ Z) : W ⟶ Z :=
-  f ≫ MonoidalCoherence.hom ≫ g
-
-@[inherit_doc Mathlib.Tactic.Coherence.monoidalComp]
-scoped[CategoryTheory.MonoidalCategory] infixr:80 " ⊗≫ " =>
-  Mathlib.Tactic.Coherence.monoidalComp -- type as \ot \gg
-
-/-- Compose two isomorphisms in a monoidal category,
-inserting unitors and associators between as necessary. -/
-noncomputable def monoidalIsoComp {W X Y Z : C} [LiftObj X] [LiftObj Y]
-    [MonoidalCoherence X Y] (f : W ≅ X) (g : Y ≅ Z) : W ≅ Z :=
-  f ≪≫ asIso MonoidalCoherence.hom ≪≫ g
-
-@[inherit_doc Mathlib.Tactic.Coherence.monoidalIsoComp]
-scoped[CategoryTheory.MonoidalCategory] infixr:80 " ≪⊗≫ " =>
-  Mathlib.Tactic.Coherence.monoidalIsoComp -- type as \ll \ot \gg
-
-example {U V W X Y : C} (f : U ⟶ V ⊗ (W ⊗ X)) (g : (V ⊗ W) ⊗ X ⟶ Y) : U ⟶ Y := f ⊗≫ g
-
--- To automatically insert unitors/associators at the beginning or end,
--- you can use `f ⊗≫ 𝟙 _`
-example {W X Y Z : C} (f : W ⟶ (X ⊗ Y) ⊗ Z) : W ⟶ X ⊗ (Y ⊗ Z) := f ⊗≫ 𝟙 _
-
-@[simp] lemma monoidalComp_refl {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z) :
-    f ⊗≫ g = f ≫ g := by
-  simp [monoidalComp]
-
-example {U V W X Y : C} (f : U ⟶ V ⊗ (W ⊗ X)) (g : (V ⊗ W) ⊗ X ⟶ Y) :
-    f ⊗≫ g = f ≫ (α_ _ _ _).inv ≫ g := by
-  simp [MonoidalCategory.tensorHom_def, monoidalComp]
-
 end lifting
 
 open Lean Meta Elab Tactic

feat(CategoryTheory/Monoidal): add whiskerings to free monoidal categories (#11172)

Since the coherence tactic assume that a certain defeq property holds for structural morphisms in a monoidal category and their corresponding morphisms in the free monoidal category, we want free monoidal categories to have the whiskering operators as primitives.

This PR also simplified the proof of the coherence theorem, and removed some porting notes.

1029b4ff

Diff

@@ -90,11 +90,11 @@ instance LiftHom_comp {X Y Z : C} [LiftObj X] [LiftObj Y] [LiftObj Z] (f : X ⟶
 
 instance liftHom_WhiskerLeft (X : C) [LiftObj X] {Y Z : C} [LiftObj Y] [LiftObj Z]
     (f : Y ⟶ Z) [LiftHom f] : LiftHom (X ◁ f) where
-  lift := 𝟙 (LiftObj.lift X) ⊗ LiftHom.lift f
+  lift := LiftObj.lift X ◁ LiftHom.lift f
 
 instance liftHom_WhiskerRight {X Y : C} (f : X ⟶ Y) [LiftObj X] [LiftObj Y] [LiftHom f]
     {Z : C} [LiftObj Z] : LiftHom (f ▷ Z) where
-  lift := LiftHom.lift f ⊗ 𝟙 (LiftObj.lift Z)
+  lift := LiftHom.lift f ▷ LiftObj.lift Z
 
 instance LiftHom_tensor {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y] [LiftObj Z]
     (f : W ⟶ X) (g : Y ⟶ Z) [LiftHom f] [LiftHom g] : LiftHom (f ⊗ g) where
@@ -119,22 +119,22 @@ instance refl (X : C) [LiftObj X] : MonoidalCoherence X X := ⟨𝟙 _⟩
 @[simps]
 instance whiskerLeft (X Y Z : C) [LiftObj X] [LiftObj Y] [LiftObj Z] [MonoidalCoherence Y Z] :
     MonoidalCoherence (X ⊗ Y) (X ⊗ Z) :=
-  ⟨𝟙 X ⊗ MonoidalCoherence.hom⟩
+  ⟨X ◁ MonoidalCoherence.hom⟩
 
 @[simps]
 instance whiskerRight (X Y Z : C) [LiftObj X] [LiftObj Y] [LiftObj Z] [MonoidalCoherence X Y] :
     MonoidalCoherence (X ⊗ Z) (Y ⊗ Z) :=
-  ⟨MonoidalCoherence.hom ⊗ 𝟙 Z⟩
+  ⟨MonoidalCoherence.hom ▷ Z⟩
 
 @[simps]
 instance tensor_right (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence (𝟙_ C) Y] :
     MonoidalCoherence X (X ⊗ Y) :=
-  ⟨(ρ_ X).inv ≫ (𝟙 X ⊗  MonoidalCoherence.hom)⟩
+  ⟨(ρ_ X).inv ≫ X ◁  MonoidalCoherence.hom⟩
 
 @[simps]
 instance tensor_right' (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence Y (𝟙_ C)] :
     MonoidalCoherence (X ⊗ Y) X :=
-  ⟨(𝟙 X ⊗ MonoidalCoherence.hom) ≫ (ρ_ X).hom⟩
+  ⟨X ◁ MonoidalCoherence.hom ≫ (ρ_ X).hom⟩
 
 @[simps]
 instance left (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence X Y] :
@@ -412,9 +412,5 @@ elab_rules : tactic
       Mathlib.Tactic.BicategoryCoherence.BicategoricalCoherence.hom',
       monoidalComp]);
     whisker_simps (config := {failIfUnchanged := false});
-    monoidal_simps (config := {failIfUnchanged := false});
-    -- Workaround until we define the whiskerings as the primitives in free monoidal categories.
-    simp (config := {failIfUnchanged := false}) only
-      [← MonoidalCategory.id_tensorHom, ← MonoidalCategory.tensorHom_id]
-    ))
+    monoidal_simps (config := {failIfUnchanged := false})))
   coherence_loop

refactor(CategoryTheory/Monoidal/Rigid): use monoidalComp in the proofs (#10326)

Similar to #10078

cda31e7e

Diff

@@ -180,6 +180,10 @@ example (X1 X2 X3 X4 X5 X6 X7 X8 X9 : C) :
     (X1 ⊗ (X2 ⊗ X3) ⊗ X4 ⊗ (X5 ⊗ (𝟙_ C ⊗ X6) ⊗ X7) ⊗ X8 ⊗ X9) :=
   monoidalIso _ _
 
+/-- Notation for identities up to unitors and associators. -/
+scoped[CategoryTheory.MonoidalCategory] notation " ⊗𝟙 " =>
+  Mathlib.Tactic.Coherence.MonoidalCoherence.hom -- type as \ot 𝟙
+
 /-- Compose two morphisms in a monoidal category,
 inserting unitors and associators between as necessary. -/
 def monoidalComp {W X Y Z : C} [LiftObj X] [LiftObj Y]

refactor(CategoryTheory/Monoidal/Braided): use monoidalComp in the proofs (#10078)

depends on: #10061

007ad742

Diff

@@ -90,11 +90,11 @@ instance LiftHom_comp {X Y Z : C} [LiftObj X] [LiftObj Y] [LiftObj Z] (f : X ⟶
 
 instance liftHom_WhiskerLeft (X : C) [LiftObj X] {Y Z : C} [LiftObj Y] [LiftObj Z]
     (f : Y ⟶ Z) [LiftHom f] : LiftHom (X ◁ f) where
-  lift := LiftObj.lift X ◁ LiftHom.lift f
+  lift := 𝟙 (LiftObj.lift X) ⊗ LiftHom.lift f
 
 instance liftHom_WhiskerRight {X Y : C} (f : X ⟶ Y) [LiftObj X] [LiftObj Y] [LiftHom f]
     {Z : C} [LiftObj Z] : LiftHom (f ▷ Z) where
-  lift := LiftHom.lift f ▷ LiftObj.lift Z
+  lift := LiftHom.lift f ⊗ 𝟙 (LiftObj.lift Z)
 
 instance LiftHom_tensor {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y] [LiftObj Z]
     (f : W ⟶ X) (g : Y ⟶ Z) [LiftHom f] [LiftHom g] : LiftHom (f ⊗ g) where
@@ -129,12 +129,12 @@ instance whiskerRight (X Y Z : C) [LiftObj X] [LiftObj Y] [LiftObj Z] [MonoidalC
 @[simps]
 instance tensor_right (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence (𝟙_ C) Y] :
     MonoidalCoherence X (X ⊗ Y) :=
-  ⟨(ρ_ X).inv ≫ (X ◁  MonoidalCoherence.hom)⟩
+  ⟨(ρ_ X).inv ≫ (𝟙 X ⊗  MonoidalCoherence.hom)⟩
 
 @[simps]
 instance tensor_right' (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence Y (𝟙_ C)] :
     MonoidalCoherence (X ⊗ Y) X :=
-  ⟨(X ◁ MonoidalCoherence.hom) ≫ (ρ_ X).hom⟩
+  ⟨(𝟙 X ⊗ MonoidalCoherence.hom) ≫ (ρ_ X).hom⟩
 
 @[simps]
 instance left (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence X Y] :
@@ -362,6 +362,27 @@ def coherence_loop (maxSteps := 37) : TacticM Unit :=
       -- and whose second terms can be identified by recursively called `coherence`.
       coherence_loop maxSteps'
 
+open Lean.Parser.Tactic
+
+/--
+Simp lemmas for rewriting a hom in monoical categories into a normal form.
+-/
+syntax (name := monoidal_simps) "monoidal_simps" (config)? : tactic
+
+@[inherit_doc monoidal_simps]
+elab_rules : tactic
+| `(tactic| monoidal_simps $[$cfg]?) => do
+  evalTactic (← `(tactic|
+    simp $[$cfg]? only [
+      Category.assoc, MonoidalCategory.tensor_whiskerLeft, MonoidalCategory.id_whiskerLeft,
+      MonoidalCategory.whiskerRight_tensor, MonoidalCategory.whiskerRight_id,
+      MonoidalCategory.whiskerLeft_comp, MonoidalCategory.whiskerLeft_id,
+      MonoidalCategory.comp_whiskerRight, MonoidalCategory.id_whiskerRight,
+      MonoidalCategory.whisker_assoc];
+    -- I'm not sure if `tensorHom` should be expanded.
+    try simp only [MonoidalCategory.tensorHom_def]
+    ))
+
 /--
 Use the coherence theorem for monoidal categories to solve equations in a monoidal equation,
 where the two sides only differ by replacing strings of monoidal structural morphisms
@@ -386,6 +407,10 @@ elab_rules : tactic
       Mathlib.Tactic.BicategoryCoherence.BicategoricalCoherence.hom,
       Mathlib.Tactic.BicategoryCoherence.BicategoricalCoherence.hom',
       monoidalComp]);
-    whisker_simps (config := {failIfUnchanged := false})
+    whisker_simps (config := {failIfUnchanged := false});
+    monoidal_simps (config := {failIfUnchanged := false});
+    -- Workaround until we define the whiskerings as the primitives in free monoidal categories.
+    simp (config := {failIfUnchanged := false}) only
+      [← MonoidalCategory.id_tensorHom, ← MonoidalCategory.tensorHom_id]
     ))
   coherence_loop

feat(CategoryTheory/Monoidal): add lemmas for the whiskerings (#9995)

Extracted from #6307.

f1919fd4

Diff

@@ -88,6 +88,14 @@ instance LiftHom_comp {X Y Z : C} [LiftObj X] [LiftObj Y] [LiftObj Z] (f : X ⟶
     [LiftHom f] [LiftHom g] : LiftHom (f ≫ g) where
   lift := LiftHom.lift f ≫ LiftHom.lift g
 
+instance liftHom_WhiskerLeft (X : C) [LiftObj X] {Y Z : C} [LiftObj Y] [LiftObj Z]
+    (f : Y ⟶ Z) [LiftHom f] : LiftHom (X ◁ f) where
+  lift := LiftObj.lift X ◁ LiftHom.lift f
+
+instance liftHom_WhiskerRight {X Y : C} (f : X ⟶ Y) [LiftObj X] [LiftObj Y] [LiftHom f]
+    {Z : C} [LiftObj Z] : LiftHom (f ▷ Z) where
+  lift := LiftHom.lift f ▷ LiftObj.lift Z
+
 instance LiftHom_tensor {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y] [LiftObj Z]
     (f : W ⟶ X) (g : Y ⟶ Z) [LiftHom f] [LiftHom g] : LiftHom (f ⊗ g) where
   lift := LiftHom.lift f ⊗ LiftHom.lift g
@@ -109,19 +117,24 @@ namespace MonoidalCoherence
 instance refl (X : C) [LiftObj X] : MonoidalCoherence X X := ⟨𝟙 _⟩
 
 @[simps]
-instance tensor (X Y Z : C) [LiftObj X] [LiftObj Y] [LiftObj Z] [MonoidalCoherence Y Z] :
+instance whiskerLeft (X Y Z : C) [LiftObj X] [LiftObj Y] [LiftObj Z] [MonoidalCoherence Y Z] :
     MonoidalCoherence (X ⊗ Y) (X ⊗ Z) :=
   ⟨𝟙 X ⊗ MonoidalCoherence.hom⟩
 
+@[simps]
+instance whiskerRight (X Y Z : C) [LiftObj X] [LiftObj Y] [LiftObj Z] [MonoidalCoherence X Y] :
+    MonoidalCoherence (X ⊗ Z) (Y ⊗ Z) :=
+  ⟨MonoidalCoherence.hom ⊗ 𝟙 Z⟩
+
 @[simps]
 instance tensor_right (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence (𝟙_ C) Y] :
     MonoidalCoherence X (X ⊗ Y) :=
-  ⟨(ρ_ X).inv ≫ (𝟙 X ⊗ MonoidalCoherence.hom)⟩
+  ⟨(ρ_ X).inv ≫ (X ◁  MonoidalCoherence.hom)⟩
 
 @[simps]
 instance tensor_right' (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence Y (𝟙_ C)] :
     MonoidalCoherence (X ⊗ Y) X :=
-  ⟨(𝟙 X ⊗ MonoidalCoherence.hom) ≫ (ρ_ X).hom⟩
+  ⟨(X ◁ MonoidalCoherence.hom) ≫ (ρ_ X).hom⟩
 
 @[simps]
 instance left (X Y : C) [LiftObj X] [LiftObj Y] [MonoidalCoherence X Y] :
@@ -199,7 +212,7 @@ example {W X Y Z : C} (f : W ⟶ (X ⊗ Y) ⊗ Z) : W ⟶ X ⊗ (Y ⊗ Z) := f 
 
 example {U V W X Y : C} (f : U ⟶ V ⊗ (W ⊗ X)) (g : (V ⊗ W) ⊗ X ⟶ Y) :
     f ⊗≫ g = f ≫ (α_ _ _ _).inv ≫ g := by
-  simp [monoidalComp]
+  simp [MonoidalCategory.tensorHom_def, monoidalComp]
 
 end lifting
 
@@ -227,7 +240,7 @@ def mkProjectMapExpr (e : Expr) : TermElabM Expr := do
 /-- Coherence tactic for monoidal categories. -/
 def monoidal_coherence (g : MVarId) : TermElabM Unit := g.withContext do
   withOptions (fun opts => synthInstance.maxSize.set opts
-    (max 256 (synthInstance.maxSize.get opts))) do
+    (max 512 (synthInstance.maxSize.get opts))) do
   -- TODO: is this `dsimp only` step necessary? It doesn't appear to be in the tests below.
   let (ty, _) ← dsimp (← g.getType) (← Simp.Context.ofNames [] true)
   let some (_, lhs, rhs) := (← whnfR ty).eq? | exception g "Not an equation of morphisms."

chore: reduce imports (#9830)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

f4c4ca61

Diff

@@ -3,7 +3,8 @@ Copyright (c) 2022. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Yuma Mizuno, Oleksandr Manzyuk
 -/
-import Mathlib.CategoryTheory.Monoidal.Free.Coherence
+import Mathlib.CategoryTheory.Monoidal.Free.Basic
+import Mathlib.Lean.Meta
 import Mathlib.Tactic.CategoryTheory.BicategoryCoherence
 
 #align_import category_theory.monoidal.coherence from "leanprover-community/mathlib"@"f187f1074fa1857c94589cc653c786cadc4c35ff"

chore: use string gaps (#9193)

For error messages that span multiple lines, now we can use the new "string gap" escape sequence (a \ at the end of the line, which causes all the whitespace at the beginning of the next line ignored), rather than using append operations or hacks involving { and } for s! and m! strings.

Style-wise, we suggest for long messages that the body of the message start on the next line if possible, by starting the message with a string gap sequence. This eliminates needing to decide whether to indent continuing lines at the " or at the next column. For example:

    logError m!"\
      Tactic 'more_magic' cannot \
      apply expression{indentD e}\n\
      due to some reason or another."

Note that to get whitespace to appear between one line and the next, you include it before the \.

16877b9c

Diff

@@ -329,8 +329,8 @@ def coherence_loop (maxSteps := 37) : TacticM Unit :=
     -- Otherwise, rearrange so we have a maximal prefix of each side
     -- that is built out of unitors and associators:
     evalTactic (← `(tactic| liftable_prefixes)) <|>
-      exception' ("Something went wrong in the `coherence` tactic: " ++
-        "is the target an equation in a monoidal category?")
+      exception' "Something went wrong in the `coherence` tactic: \
+        is the target an equation in a monoidal category?"
     -- The goal should now look like `f₀ ≫ f₁ = g₀ ≫ g₁`,
     liftMetaTactic MVarId.congrCore
     -- and now we have two goals `f₀ = g₀` and `f₁ = g₁`.

fix: lean4-ify names of inductive constructors (#8652)

These inductive types carry data, so these should be functionCase not theorem_case.

It seems that mathport didn't do this.

79254c97

Diff

@@ -49,7 +49,7 @@ It must be the case that `projectObj id (LiftObj.lift x) = x` by defeq. -/
 class LiftObj (X : C) where
   protected lift : FreeMonoidalCategory C
 
-instance LiftObj_unit : LiftObj (𝟙_ C) := ⟨Unit⟩
+instance LiftObj_unit : LiftObj (𝟙_ C) := ⟨unit⟩
 
 instance LiftObj_tensor (X Y : C) [LiftObj X] [LiftObj Y] : LiftObj (X ⊗ Y) where
   lift := LiftObj.lift X ⊗ LiftObj.lift Y

feat(CategoryTheory/Bicategory): define adjunctions (#6406)

This RP introduces adjunctions and adjoint equivalences in bicategories, and shows that a (non-adjoint) equivalence can be promoted to an adjoint equivalence by upgrading the counit.

The constructor of adjoint equivalences only requires the left triangle identities since I will plan to show that it implies the right triangle identities in a separate PR.

2afbd9d8

Diff

@@ -172,8 +172,9 @@ def monoidalComp {W X Y Z : C} [LiftObj X] [LiftObj Y]
     [MonoidalCoherence X Y] (f : W ⟶ X) (g : Y ⟶ Z) : W ⟶ Z :=
   f ≫ MonoidalCoherence.hom ≫ g
 
-@[inherit_doc monoidalComp]
-infixr:80 " ⊗≫ " => monoidalComp -- type as \ot \gg
+@[inherit_doc Mathlib.Tactic.Coherence.monoidalComp]
+scoped[CategoryTheory.MonoidalCategory] infixr:80 " ⊗≫ " =>
+  Mathlib.Tactic.Coherence.monoidalComp -- type as \ot \gg
 
 /-- Compose two isomorphisms in a monoidal category,
 inserting unitors and associators between as necessary. -/
@@ -181,8 +182,9 @@ noncomputable def monoidalIsoComp {W X Y Z : C} [LiftObj X] [LiftObj Y]
     [MonoidalCoherence X Y] (f : W ≅ X) (g : Y ≅ Z) : W ≅ Z :=
   f ≪≫ asIso MonoidalCoherence.hom ≪≫ g
 
-@[inherit_doc monoidalIsoComp]
-infixr:80 " ≪⊗≫ " => monoidalIsoComp -- type as \ot \gg
+@[inherit_doc Mathlib.Tactic.Coherence.monoidalIsoComp]
+scoped[CategoryTheory.MonoidalCategory] infixr:80 " ≪⊗≫ " =>
+  Mathlib.Tactic.Coherence.monoidalIsoComp -- type as \ll \ot \gg
 
 example {U V W X Y : C} (f : U ⟶ V ⊗ (W ⊗ X)) (g : (V ⊗ W) ⊗ X ⟶ Y) : U ⟶ Y := f ⊗≫ g
 
@@ -366,7 +368,10 @@ syntax (name := coherence) "coherence" : tactic
 elab_rules : tactic
 | `(tactic| coherence) => do
   evalTactic (← `(tactic|
-    (simp (config := {failIfUnchanged := false}) only [bicategoricalComp, monoidalComp]);
+    (simp (config := {failIfUnchanged := false}) only [bicategoricalComp,
+      Mathlib.Tactic.BicategoryCoherence.BicategoricalCoherence.hom,
+      Mathlib.Tactic.BicategoryCoherence.BicategoricalCoherence.hom',
+      monoidalComp]);
     whisker_simps (config := {failIfUnchanged := false})
     ))
   coherence_loop

chore: bump to nightly-2023-08-17 (#6019)

The major change here is adapting to simp failing if it makes no progress. The vast majority of the redundant simps found due to this change were extracted to #6632.

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

8c53b718

Diff

@@ -287,9 +287,11 @@ elab (name := liftable_prefixes) "liftable_prefixes" : tactic => do
   withOptions (fun opts => synthInstance.maxSize.set opts
     (max 256 (synthInstance.maxSize.get opts))) do
   evalTactic (← `(tactic|
-    simp only [monoidalComp, Category.assoc, MonoidalCoherence.hom] <;>
+    (simp (config := {failIfUnchanged := false}) only
+      [monoidalComp, Category.assoc, MonoidalCoherence.hom]) <;>
     (apply (cancel_epi (𝟙 _)).1 <;> try infer_instance) <;>
-    simp only [assoc_liftHom, Mathlib.Tactic.BicategoryCoherence.assoc_liftHom₂]))
+    (simp (config := {failIfUnchanged := false}) only
+      [assoc_liftHom, Mathlib.Tactic.BicategoryCoherence.assoc_liftHom₂])))
 
 lemma insert_id_lhs {C : Type*} [Category C] {X Y : C} (f g : X ⟶ Y) (w : f ≫ 𝟙 _ = g) :
     f = g := by
@@ -364,8 +366,7 @@ syntax (name := coherence) "coherence" : tactic
 elab_rules : tactic
 | `(tactic| coherence) => do
   evalTactic (← `(tactic|
-    simp only [bicategoricalComp];
-    simp only [monoidalComp];
-    try whisker_simps
+    (simp (config := {failIfUnchanged := false}) only [bicategoricalComp, monoidalComp]);
+    whisker_simps (config := {failIfUnchanged := false})
     ))
   coherence_loop

fix: disable autoImplicit globally (#6528)

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

Assuming variables are in scope, but pasting the lemma in the wrong section
Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

0c24f831

Diff

@@ -26,6 +26,8 @@ which automatically inserts associators and unitors as needed
 to make the target of `f` match the source of `g`.
 -/
 
+set_option autoImplicit true
+
 -- Porting note: restore when ported
 -- import Mathlib.CategoryTheory.Bicategory.CoherenceTactic

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -289,11 +289,11 @@ elab (name := liftable_prefixes) "liftable_prefixes" : tactic => do
     (apply (cancel_epi (𝟙 _)).1 <;> try infer_instance) <;>
     simp only [assoc_liftHom, Mathlib.Tactic.BicategoryCoherence.assoc_liftHom₂]))
 
-lemma insert_id_lhs {C : Type _} [Category C] {X Y : C} (f g : X ⟶ Y) (w : f ≫ 𝟙 _ = g) :
+lemma insert_id_lhs {C : Type*} [Category C] {X Y : C} (f g : X ⟶ Y) (w : f ≫ 𝟙 _ = g) :
     f = g := by
   simpa using w
 
-lemma insert_id_rhs {C : Type _} [Category C] {X Y : C} (f g : X ⟶ Y) (w : f = g ≫ 𝟙 _) :
+lemma insert_id_rhs {C : Type*} [Category C] {X Y : C} (f g : X ⟶ Y) (w : f = g ≫ 𝟙 _) :
     f = g := by
   simpa using w

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Yuma Mizuno, Oleksandr Manzyuk
-
-! This file was ported from Lean 3 source module category_theory.monoidal.coherence
-! leanprover-community/mathlib commit f187f1074fa1857c94589cc653c786cadc4c35ff
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Monoidal.Free.Coherence
 import Mathlib.Tactic.CategoryTheory.BicategoryCoherence
 
+#align_import category_theory.monoidal.coherence from "leanprover-community/mathlib"@"f187f1074fa1857c94589cc653c786cadc4c35ff"
+
 /-!
 # A `coherence` tactic for monoidal categories, and `⊗≫` (composition up to associators)

chore: formatting issues (#4947)

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

5068808d

Diff

@@ -292,11 +292,13 @@ elab (name := liftable_prefixes) "liftable_prefixes" : tactic => do
     (apply (cancel_epi (𝟙 _)).1 <;> try infer_instance) <;>
     simp only [assoc_liftHom, Mathlib.Tactic.BicategoryCoherence.assoc_liftHom₂]))
 
-lemma insert_id_lhs {C : Type _} [Category C] {X Y : C} (f g : X ⟶ Y) (w : f ≫ 𝟙 _ = g) : f = g :=
-by simpa using w
+lemma insert_id_lhs {C : Type _} [Category C] {X Y : C} (f g : X ⟶ Y) (w : f ≫ 𝟙 _ = g) :
+    f = g := by
+  simpa using w
 
-lemma insert_id_rhs {C : Type _} [Category C] {X Y : C} (f g : X ⟶ Y) (w : f = g ≫ 𝟙 _) : f = g :=
-by simpa using w
+lemma insert_id_rhs {C : Type _} [Category C] {X Y : C} (f g : X ⟶ Y) (w : f = g ≫ 𝟙 _) :
+    f = g := by
+  simpa using w
 
 /-- If either the lhs or rhs is not a composition, compose it on the right with an identity. -/
 def insertTrailingIds (g : MVarId) : MetaM MVarId := do

feat: port CategoryTheory.Bicategory.CoherenceTactic (#4610)

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

b59f0ddb

Diff

@@ -9,6 +9,7 @@ Authors: Scott Morrison, Yuma Mizuno, Oleksandr Manzyuk
 ! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Monoidal.Free.Coherence
+import Mathlib.Tactic.CategoryTheory.BicategoryCoherence
 
 /-!
 # A `coherence` tactic for monoidal categories, and `⊗≫` (composition up to associators)
@@ -40,6 +41,7 @@ open CategoryTheory FreeMonoidalCategory
 namespace Mathlib.Tactic.Coherence
 
 variable {C : Type u} [Category.{v} C] [MonoidalCategory C]
+open scoped MonoidalCategory
 
 noncomputable section lifting
 
@@ -241,6 +243,8 @@ def monoidal_coherence (g : MVarId) : TermElabM Unit := g.withContext do
 Use `pure_coherence` instead, which is a frontend to this one. -/
 elab "monoidal_coherence" : tactic => do monoidal_coherence (← getMainGoal)
 
+open Mathlib.Tactic.BicategoryCoherence
+
 /--
 `pure_coherence` uses the coherence theorem for monoidal categories to prove the goal.
 It can prove any equality made up only of associators, unitors, and identities.
@@ -255,12 +259,9 @@ which can also cope with identities of the form
 `a ≫ f ≫ b ≫ g ≫ c = a' ≫ f ≫ b' ≫ g ≫ c'`
 where `a = a'`, `b = b'`, and `c = c'` can be proved using `pure_coherence`
 -/
-macro (name := pure_coherence) "pure_coherence" : tactic =>
-  `(tactic| monoidal_coherence)
-
--- Porting note: restore this when `category_theory.bicategory.coherence` is ported.
--- macro (name := pure_coherence') "pure_coherence" : tactic =>
---   `(tactic| bicategory_coherence)
+elab (name := pure_coherence) "pure_coherence" : tactic => do
+  let g ← getMainGoal
+  monoidal_coherence g <|> bicategory_coherence g
 
 /--
 Auxiliary simp lemma for the `coherence` tactic:
@@ -271,7 +272,7 @@ built out of unitors and associators.
 -- They are intentional, to ensure that `simp only [assoc_LiftHom]` only left associates
 -- monoidal structural morphisms.
 @[nolint unusedArguments]
-lemma assoc_LiftHom {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y]
+lemma assoc_liftHom {W X Y Z : C} [LiftObj W] [LiftObj X] [LiftObj Y]
     (f : W ⟶ X) (g : X ⟶ Y) (h : Y ⟶ Z) [LiftHom f] [LiftHom g] :
     f ≫ (g ≫ h) = (f ≫ g) ≫ h :=
   (Category.assoc _ _ _).symm
@@ -289,9 +290,7 @@ elab (name := liftable_prefixes) "liftable_prefixes" : tactic => do
   evalTactic (← `(tactic|
     simp only [monoidalComp, Category.assoc, MonoidalCoherence.hom] <;>
     (apply (cancel_epi (𝟙 _)).1 <;> try infer_instance) <;>
-    -- TODO add `Bicategory.Coherence.assoc_LiftHom₂` when
-    -- `category_theory.bicategory.coherence` is ported.
-    simp only [assoc_LiftHom]))
+    simp only [assoc_liftHom, Mathlib.Tactic.BicategoryCoherence.assoc_liftHom₂]))
 
 lemma insert_id_lhs {C : Type _} [Category C] {X Y : C} (f g : X ⟶ Y) (w : f ≫ 𝟙 _ = g) : f = g :=
 by simpa using w
@@ -332,7 +331,7 @@ def coherence_loop (maxSteps := 37) : TacticM Unit :=
     -- and now we have two goals `f₀ = g₀` and `f₁ = g₁`.
     -- Discharge the first using `coherence`,
     evalTactic (← `(tactic| { pure_coherence })) <|>
-      exception' "`coherence` tactic failed, subgoal not true in the free monoidal_category"
+      exception' "`coherence` tactic failed, subgoal not true in the free monoidal category"
     -- Then check that either `g₀` is identically `g₁`,
     evalTactic (← `(tactic| rfl)) <|> do
       -- or that both are compositions,
@@ -364,10 +363,8 @@ syntax (name := coherence) "coherence" : tactic
 elab_rules : tactic
 | `(tactic| coherence) => do
   evalTactic (← `(tactic|
-    -- Porting note: restore this when `category_theory.bicategory.coherence` is ported.
-    -- simp only [bicategorical_comp];
-    simp only [monoidalComp]
-    -- Porting note: restore this when `category_theory.bicategory.coherence` is ported.
-    -- try bicategory.whisker_simps
+    simp only [bicategoricalComp];
+    simp only [monoidalComp];
+    try whisker_simps
     ))
   coherence_loop

feat: port CategoryTheory.Monoidal.Braided (#4560)

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

b265a524

Diff

@@ -283,14 +283,15 @@ Rewrites an equation `f = g` as `f₀ ≫ f₁ = g₀ ≫ g₁`,
 where `f₀` and `g₀` are maximal prefixes of `f` and `g` (possibly after reassociating)
 which are "liftable" (i.e. expressible as compositions of unitors and associators).
 -/
-macro (name := liftable_prefixes) "liftable_prefixes" : tactic => do
-  -- TODO we used to set the max instance search depth higher. Is this still needed?
-  `(tactic|
+elab (name := liftable_prefixes) "liftable_prefixes" : tactic => do
+  withOptions (fun opts => synthInstance.maxSize.set opts
+    (max 256 (synthInstance.maxSize.get opts))) do
+  evalTactic (← `(tactic|
     simp only [monoidalComp, Category.assoc, MonoidalCoherence.hom] <;>
     (apply (cancel_epi (𝟙 _)).1 <;> try infer_instance) <;>
     -- TODO add `Bicategory.Coherence.assoc_LiftHom₂` when
     -- `category_theory.bicategory.coherence` is ported.
-    simp only [assoc_LiftHom])
+    simp only [assoc_LiftHom]))
 
 lemma insert_id_lhs {C : Type _} [Category C] {X Y : C} (f g : X ⟶ Y) (w : f ≫ 𝟙 _ = g) : f = g :=
 by simpa using w

chore: fix many typos (#4535)

Run codespell Mathlib and keep some suggestions.

92f5c622

Diff

@@ -212,7 +212,7 @@ def exception' (msg : MessageData) : TacticM Unit := do
     -- There might not be any goals
     throwError msg
 
-/-- Auxilliary definition for `monoidal_coherence`. -/
+/-- Auxiliary definition for `monoidal_coherence`. -/
 -- We could construct this expression directly without using `elabTerm`,
 -- but it would require preparing many implicit arguments by hand.
 def mkProjectMapExpr (e : Expr) : TermElabM Expr := do