category_theory.monoidal.of_has_finite_products

Changes since the initial port

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.

Changes in mathlib3

f153a85a

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

6b31d1ee

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Simon Hudon
 -/
-import CategoryTheory.Monoidal.Braided
+import CategoryTheory.Monoidal.Braided.Basic
 import CategoryTheory.Limits.Shapes.BinaryProducts
 import CategoryTheory.Limits.Shapes.Terminal

6b31d1ee

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Simon Hudon
 -/
-import Mathbin.CategoryTheory.Monoidal.Braided
-import Mathbin.CategoryTheory.Limits.Shapes.BinaryProducts
-import Mathbin.CategoryTheory.Limits.Shapes.Terminal
+import CategoryTheory.Monoidal.Braided
+import CategoryTheory.Limits.Shapes.BinaryProducts
+import CategoryTheory.Limits.Shapes.Terminal
 
 #align_import category_theory.monoidal.of_has_finite_products from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"

6b31d1ee

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Simon Hudon
-
-! This file was ported from Lean 3 source module category_theory.monoidal.of_has_finite_products
-! 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.Braided
 import Mathbin.CategoryTheory.Limits.Shapes.BinaryProducts
 import Mathbin.CategoryTheory.Limits.Shapes.Terminal
 
+#align_import category_theory.monoidal.of_has_finite_products from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
+
 /-!
 # The natural monoidal structure on any category with finite (co)products.

6b31d1ee

bump to nightly-2023-06-10-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

e13a28eb

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Simon Hudon
 
 ! This file was ported from Lean 3 source module category_theory.monoidal.of_has_finite_products
-! leanprover-community/mathlib commit f153a85a8dc0a96ce9133fed69e34df72f7f191f
+! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.CategoryTheory.Limits.Shapes.Terminal
 /-!
 # The natural monoidal structure on any category with finite (co)products.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A category with a monoidal structure provided in this way
 is sometimes called a (co)cartesian category,
 although this is also sometimes used to mean a finitely complete category.

f153a85a

bump to nightly-2023-06-08-19

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

79d4a9a4

Diff

@@ -49,6 +49,7 @@ section
 
 attribute [local tidy] tactic.case_bash
 
+#print CategoryTheory.monoidalOfHasFiniteProducts /-
 /-- A category with a terminal object and binary products has a natural monoidal structure. -/
 def monoidalOfHasFiniteProducts [HasTerminal C] [HasBinaryProducts C] : MonoidalCategory C
     where
@@ -62,6 +63,7 @@ def monoidalOfHasFiniteProducts [HasTerminal C] [HasBinaryProducts C] : Monoidal
   triangle' := prod.triangle
   associator_naturality' := @prod.associator_naturality _ _ _
 #align category_theory.monoidal_of_has_finite_products CategoryTheory.monoidalOfHasFiniteProducts
+-/
 
 end
 
@@ -71,6 +73,7 @@ attribute [local instance] monoidal_of_has_finite_products
 
 open MonoidalCategory
 
+#print CategoryTheory.symmetricOfHasFiniteProducts /-
 /-- The monoidal structure coming from finite products is symmetric.
 -/
 @[simps]
@@ -82,6 +85,7 @@ def symmetricOfHasFiniteProducts [HasTerminal C] [HasBinaryProducts C] : Symmetr
   hexagon_reverse' X Y Z := by dsimp [monoidal_of_has_finite_products]; simp
   symmetry' X Y := by dsimp; simp; rfl
 #align category_theory.symmetric_of_has_finite_products CategoryTheory.symmetricOfHasFiniteProducts
+-/
 
 end
 
@@ -92,37 +96,50 @@ variable [HasTerminal C] [HasBinaryProducts C]
 attribute [local instance] monoidal_of_has_finite_products
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.monoidalOfHasFiniteProducts.tensorObj /-
 @[simp]
 theorem tensorObj (X Y : C) : X ⊗ Y = (X ⨯ Y) :=
   rfl
 #align category_theory.monoidal_of_has_finite_products.tensor_obj CategoryTheory.monoidalOfHasFiniteProducts.tensorObj
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.monoidalOfHasFiniteProducts.tensorHom /-
 @[simp]
 theorem tensorHom {W X Y Z : C} (f : W ⟶ X) (g : Y ⟶ Z) : f ⊗ g = Limits.prod.map f g :=
   rfl
 #align category_theory.monoidal_of_has_finite_products.tensor_hom CategoryTheory.monoidalOfHasFiniteProducts.tensorHom
+-/
 
+#print CategoryTheory.monoidalOfHasFiniteProducts.leftUnitor_hom /-
 @[simp]
 theorem leftUnitor_hom (X : C) : (λ_ X).Hom = Limits.prod.snd :=
   rfl
 #align category_theory.monoidal_of_has_finite_products.left_unitor_hom CategoryTheory.monoidalOfHasFiniteProducts.leftUnitor_hom
+-/
 
+#print CategoryTheory.monoidalOfHasFiniteProducts.leftUnitor_inv /-
 @[simp]
 theorem leftUnitor_inv (X : C) : (λ_ X).inv = prod.lift (terminal.from X) (𝟙 _) :=
   rfl
 #align category_theory.monoidal_of_has_finite_products.left_unitor_inv CategoryTheory.monoidalOfHasFiniteProducts.leftUnitor_inv
+-/
 
+#print CategoryTheory.monoidalOfHasFiniteProducts.rightUnitor_hom /-
 @[simp]
 theorem rightUnitor_hom (X : C) : (ρ_ X).Hom = Limits.prod.fst :=
   rfl
 #align category_theory.monoidal_of_has_finite_products.right_unitor_hom CategoryTheory.monoidalOfHasFiniteProducts.rightUnitor_hom
+-/
 
+#print CategoryTheory.monoidalOfHasFiniteProducts.rightUnitor_inv /-
 @[simp]
 theorem rightUnitor_inv (X : C) : (ρ_ X).inv = prod.lift (𝟙 _) (terminal.from X) :=
   rfl
 #align category_theory.monoidal_of_has_finite_products.right_unitor_inv CategoryTheory.monoidalOfHasFiniteProducts.rightUnitor_inv
+-/
 
+#print CategoryTheory.monoidalOfHasFiniteProducts.associator_hom /-
 -- We don't mark this as a simp lemma, even though in many particular
 -- categories the right hand side will simplify significantly further.
 -- For now, we'll plan to create specialised simp lemmas in each particular category.
@@ -132,6 +149,7 @@ theorem associator_hom (X Y Z : C) :
         (prod.lift (Limits.prod.fst ≫ Limits.prod.snd) Limits.prod.snd) :=
   rfl
 #align category_theory.monoidal_of_has_finite_products.associator_hom CategoryTheory.monoidalOfHasFiniteProducts.associator_hom
+-/
 
 end MonoidalOfHasFiniteProducts
 
@@ -139,6 +157,7 @@ section
 
 attribute [local tidy] tactic.case_bash
 
+#print CategoryTheory.monoidalOfHasFiniteCoproducts /-
 /-- A category with an initial object and binary coproducts has a natural monoidal structure. -/
 def monoidalOfHasFiniteCoproducts [HasInitial C] [HasBinaryCoproducts C] : MonoidalCategory C
     where
@@ -152,6 +171,7 @@ def monoidalOfHasFiniteCoproducts [HasInitial C] [HasBinaryCoproducts C] : Monoi
   triangle' := coprod.triangle
   associator_naturality' := @coprod.associator_naturality _ _ _
 #align category_theory.monoidal_of_has_finite_coproducts CategoryTheory.monoidalOfHasFiniteCoproducts
+-/
 
 end
 
@@ -161,6 +181,7 @@ attribute [local instance] monoidal_of_has_finite_coproducts
 
 open MonoidalCategory
 
+#print CategoryTheory.symmetricOfHasFiniteCoproducts /-
 /-- The monoidal structure coming from finite coproducts is symmetric.
 -/
 @[simps]
@@ -172,6 +193,7 @@ def symmetricOfHasFiniteCoproducts [HasInitial C] [HasBinaryCoproducts C] : Symm
   hexagon_reverse' X Y Z := by dsimp [monoidal_of_has_finite_coproducts]; simp
   symmetry' X Y := by dsimp; simp; rfl
 #align category_theory.symmetric_of_has_finite_coproducts CategoryTheory.symmetricOfHasFiniteCoproducts
+-/
 
 end
 
@@ -182,37 +204,50 @@ variable [HasInitial C] [HasBinaryCoproducts C]
 attribute [local instance] monoidal_of_has_finite_coproducts
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.monoidalOfHasFiniteCoproducts.tensorObj /-
 @[simp]
 theorem tensorObj (X Y : C) : X ⊗ Y = (X ⨿ Y) :=
   rfl
 #align category_theory.monoidal_of_has_finite_coproducts.tensor_obj CategoryTheory.monoidalOfHasFiniteCoproducts.tensorObj
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.monoidalOfHasFiniteCoproducts.tensorHom /-
 @[simp]
 theorem tensorHom {W X Y Z : C} (f : W ⟶ X) (g : Y ⟶ Z) : f ⊗ g = Limits.coprod.map f g :=
   rfl
 #align category_theory.monoidal_of_has_finite_coproducts.tensor_hom CategoryTheory.monoidalOfHasFiniteCoproducts.tensorHom
+-/
 
+#print CategoryTheory.monoidalOfHasFiniteCoproducts.leftUnitor_hom /-
 @[simp]
 theorem leftUnitor_hom (X : C) : (λ_ X).Hom = coprod.desc (initial.to X) (𝟙 _) :=
   rfl
 #align category_theory.monoidal_of_has_finite_coproducts.left_unitor_hom CategoryTheory.monoidalOfHasFiniteCoproducts.leftUnitor_hom
+-/
 
+#print CategoryTheory.monoidalOfHasFiniteCoproducts.rightUnitor_hom /-
 @[simp]
 theorem rightUnitor_hom (X : C) : (ρ_ X).Hom = coprod.desc (𝟙 _) (initial.to X) :=
   rfl
 #align category_theory.monoidal_of_has_finite_coproducts.right_unitor_hom CategoryTheory.monoidalOfHasFiniteCoproducts.rightUnitor_hom
+-/
 
+#print CategoryTheory.monoidalOfHasFiniteCoproducts.leftUnitor_inv /-
 @[simp]
 theorem leftUnitor_inv (X : C) : (λ_ X).inv = Limits.coprod.inr :=
   rfl
 #align category_theory.monoidal_of_has_finite_coproducts.left_unitor_inv CategoryTheory.monoidalOfHasFiniteCoproducts.leftUnitor_inv
+-/
 
+#print CategoryTheory.monoidalOfHasFiniteCoproducts.rightUnitor_inv /-
 @[simp]
 theorem rightUnitor_inv (X : C) : (ρ_ X).inv = Limits.coprod.inl :=
   rfl
 #align category_theory.monoidal_of_has_finite_coproducts.right_unitor_inv CategoryTheory.monoidalOfHasFiniteCoproducts.rightUnitor_inv
+-/
 
+#print CategoryTheory.monoidalOfHasFiniteCoproducts.associator_hom /-
 -- We don't mark this as a simp lemma, even though in many particular
 -- categories the right hand side will simplify significantly further.
 -- For now, we'll plan to create specialised simp lemmas in each particular category.
@@ -221,6 +256,7 @@ theorem associator_hom (X Y Z : C) :
       coprod.desc (coprod.desc coprod.inl (coprod.inl ≫ coprod.inr)) (coprod.inr ≫ coprod.inr) :=
   rfl
 #align category_theory.monoidal_of_has_finite_coproducts.associator_hom CategoryTheory.monoidalOfHasFiniteCoproducts.associator_hom
+-/
 
 end MonoidalOfHasFiniteCoproducts

f153a85a

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -77,19 +77,10 @@ open MonoidalCategory
 def symmetricOfHasFiniteProducts [HasTerminal C] [HasBinaryProducts C] : SymmetricCategory C
     where
   braiding X Y := Limits.prod.braiding X Y
-  braiding_naturality' X X' Y Y' f g := by
-    dsimp [tensor_hom]
-    simp
-  hexagon_forward' X Y Z := by
-    dsimp [monoidal_of_has_finite_products]
-    simp
-  hexagon_reverse' X Y Z := by
-    dsimp [monoidal_of_has_finite_products]
-    simp
-  symmetry' X Y := by
-    dsimp
-    simp
-    rfl
+  braiding_naturality' X X' Y Y' f g := by dsimp [tensor_hom]; simp
+  hexagon_forward' X Y Z := by dsimp [monoidal_of_has_finite_products]; simp
+  hexagon_reverse' X Y Z := by dsimp [monoidal_of_has_finite_products]; simp
+  symmetry' X Y := by dsimp; simp; rfl
 #align category_theory.symmetric_of_has_finite_products CategoryTheory.symmetricOfHasFiniteProducts
 
 end
@@ -176,19 +167,10 @@ open MonoidalCategory
 def symmetricOfHasFiniteCoproducts [HasInitial C] [HasBinaryCoproducts C] : SymmetricCategory C
     where
   braiding := Limits.coprod.braiding
-  braiding_naturality' X X' Y Y' f g := by
-    dsimp [tensor_hom]
-    simp
-  hexagon_forward' X Y Z := by
-    dsimp [monoidal_of_has_finite_coproducts]
-    simp
-  hexagon_reverse' X Y Z := by
-    dsimp [monoidal_of_has_finite_coproducts]
-    simp
-  symmetry' X Y := by
-    dsimp
-    simp
-    rfl
+  braiding_naturality' X X' Y Y' f g := by dsimp [tensor_hom]; simp
+  hexagon_forward' X Y Z := by dsimp [monoidal_of_has_finite_coproducts]; simp
+  hexagon_reverse' X Y Z := by dsimp [monoidal_of_has_finite_coproducts]; simp
+  symmetry' X Y := by dsimp; simp; rfl
 #align category_theory.symmetric_of_has_finite_coproducts CategoryTheory.symmetricOfHasFiniteCoproducts
 
 end

f153a85a

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

f153a85a

feat: the opposite of a braided category is braided (#10095)

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

6dc895db

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Simon Hudon
 -/
-import Mathlib.CategoryTheory.Monoidal.Braided
+import Mathlib.CategoryTheory.Monoidal.Braided.Basic
 import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
 import Mathlib.CategoryTheory.Limits.Shapes.Terminal

f153a85a

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

Extracted from #6307.

f1919fd4

Diff

@@ -82,6 +82,14 @@ theorem tensorHom {W X Y Z : C} (f : W ⟶ X) (g : Y ⟶ Z) : f ⊗ g = Limits.p
   rfl
 #align category_theory.monoidal_of_has_finite_products.tensor_hom CategoryTheory.monoidalOfHasFiniteProducts.tensorHom
 
+@[simp]
+theorem whiskerLeft (X : C) {Y Z : C} (f : Y ⟶ Z) : X ◁ f = Limits.prod.map (𝟙 X) f :=
+  rfl
+
+@[simp]
+theorem whiskerRight {X Y : C} (f : X ⟶ Y) (Z : C) : f ▷ Z = Limits.prod.map f (𝟙 Z) :=
+  rfl
+
 @[simp]
 theorem leftUnitor_hom (X : C) : (λ_ X).hom = Limits.prod.snd :=
   rfl
@@ -179,6 +187,14 @@ theorem tensorHom {W X Y Z : C} (f : W ⟶ X) (g : Y ⟶ Z) : f ⊗ g = Limits.c
   rfl
 #align category_theory.monoidal_of_has_finite_coproducts.tensor_hom CategoryTheory.monoidalOfHasFiniteCoproducts.tensorHom
 
+@[simp]
+theorem whiskerLeft (X : C) {Y Z : C} (f : Y ⟶ Z) : X ◁ f = Limits.coprod.map (𝟙 X) f :=
+  rfl
+
+@[simp]
+theorem whiskerRight {X Y : C} (f : X ⟶ Y) (Z : C) : f ▷ Z = Limits.coprod.map f (𝟙 Z) :=
+  rfl
+
 @[simp]
 theorem leftUnitor_hom (X : C) : (λ_ X).hom = coprod.desc (initial.to X) (𝟙 _) :=
   rfl

f153a85a

refactor(CategoryTheory/Monoidal): replace axioms with those more suitable for the whiskerings (#9991)

Extracted from #6307. We replace some axioms by those more preferable when using the whiskerings instead of the tensor of morphisms.

d3da7bbc

Diff

@@ -130,7 +130,8 @@ open MonoidalCategory
 @[simps]
 def symmetricOfHasFiniteProducts [HasTerminal C] [HasBinaryProducts C] : SymmetricCategory C where
   braiding X Y := Limits.prod.braiding X Y
-  braiding_naturality f g := by dsimp [tensorHom]; simp
+  braiding_naturality_left f X := by simp
+  braiding_naturality_right X _ _ f := by simp
   hexagon_forward X Y Z := by dsimp [monoidalOfHasFiniteProducts.associator_hom]; simp
   hexagon_reverse X Y Z := by dsimp [monoidalOfHasFiniteProducts.associator_inv]; simp
   symmetry X Y := by dsimp; simp
@@ -226,7 +227,8 @@ open MonoidalCategory
 def symmetricOfHasFiniteCoproducts [HasInitial C] [HasBinaryCoproducts C] :
     SymmetricCategory C where
   braiding := Limits.coprod.braiding
-  braiding_naturality f g := by dsimp [tensorHom]; simp
+  braiding_naturality_left f g := by simp
+  braiding_naturality_right f g := by simp
   hexagon_forward X Y Z := by dsimp [monoidalOfHasFiniteCoproducts.associator_hom]; simp
   hexagon_reverse X Y Z := by dsimp [monoidalOfHasFiniteCoproducts.associator_inv]; simp
   symmetry X Y := by dsimp; simp

f153a85a

refactor: Move the data fields of MonoidalCategory into a Struct class (#7279)

This matches the approach for CategoryStruct, and allows us to use the notation within MonoidalCategory.

It also makes it easier to induce the lawful structure along a faithful functor, as again it means by the time we are providing the proof fields, the notation is already available.

This also eliminates tensorUnit vs tensorUnit', adding a custom pretty-printer to provide the unprimed version with appropriate notation.

f81eaba3

Diff

@@ -46,13 +46,17 @@ section
 
 /-- A category with a terminal object and binary products has a natural monoidal structure. -/
 def monoidalOfHasFiniteProducts [HasTerminal C] [HasBinaryProducts C] : MonoidalCategory C :=
+  letI : MonoidalCategoryStruct C := {
+    tensorObj := fun X Y ↦ X ⨯ Y
+    whiskerLeft := fun X _ _ g ↦ Limits.prod.map (𝟙 _) g
+    whiskerRight := fun {_ _} f Y ↦ Limits.prod.map f (𝟙 _)
+    tensorHom := fun f g ↦ Limits.prod.map f g
+    tensorUnit := ⊤_ C
+    associator := prod.associator
+    leftUnitor := fun P ↦ prod.leftUnitor P
+    rightUnitor := fun P ↦ prod.rightUnitor P
+  }
   .ofTensorHom
-    (tensorUnit' := ⊤_ C)
-    (tensorObj := fun X Y ↦ X ⨯ Y)
-    (tensorHom := fun f g ↦ Limits.prod.map f g)
-    (associator := prod.associator)
-    (leftUnitor := fun P ↦ prod.leftUnitor P)
-    (rightUnitor := fun P ↦ prod.rightUnitor P)
     (pentagon := prod.pentagon)
     (triangle := prod.triangle)
     (associator_naturality := @prod.associator_naturality _ _ _)
@@ -138,13 +142,17 @@ section
 
 /-- A category with an initial object and binary coproducts has a natural monoidal structure. -/
 def monoidalOfHasFiniteCoproducts [HasInitial C] [HasBinaryCoproducts C] : MonoidalCategory C :=
+  letI : MonoidalCategoryStruct C := {
+    tensorObj := fun X Y ↦ X ⨿ Y
+    whiskerLeft := fun X _ _ g ↦ Limits.coprod.map (𝟙 _) g
+    whiskerRight := fun {_ _} f Y ↦ Limits.coprod.map f (𝟙 _)
+    tensorHom := fun f g ↦ Limits.coprod.map f g
+    tensorUnit := ⊥_ C
+    associator := coprod.associator
+    leftUnitor := fun P ↦ coprod.leftUnitor P
+    rightUnitor := fun P ↦ coprod.rightUnitor P
+  }
   .ofTensorHom
-    (tensorUnit' := ⊥_ C)
-    (tensorObj := fun X Y ↦ X ⨿ Y)
-    (tensorHom := fun f g ↦ Limits.coprod.map f g)
-    (associator := coprod.associator)
-    (leftUnitor := coprod.leftUnitor)
-    (rightUnitor := coprod.rightUnitor)
     (pentagon := coprod.pentagon)
     (triangle := coprod.triangle)
     (associator_naturality := @coprod.associator_naturality _ _ _)

f153a85a

feat(CategoryTheory/Monoidal): define whiskering operators (#6420)

Extracted from #6307. Just put the whiskerings into the constructor.

763106d3

Diff

@@ -45,39 +45,21 @@ open CategoryTheory.Limits
 section
 
 /-- A category with a terminal object and binary products has a natural monoidal structure. -/
-def monoidalOfHasFiniteProducts [HasTerminal C] [HasBinaryProducts C] : MonoidalCategory C where
-  tensorUnit' := ⊤_ C
-  tensorObj X Y := X ⨯ Y
-  tensorHom f g := Limits.prod.map f g
-  associator := prod.associator
-  leftUnitor P := prod.leftUnitor P
-  rightUnitor P := prod.rightUnitor P
-  pentagon := prod.pentagon
-  triangle := prod.triangle
-  associator_naturality := @prod.associator_naturality _ _ _
+def monoidalOfHasFiniteProducts [HasTerminal C] [HasBinaryProducts C] : MonoidalCategory C :=
+  .ofTensorHom
+    (tensorUnit' := ⊤_ C)
+    (tensorObj := fun X Y ↦ X ⨯ Y)
+    (tensorHom := fun f g ↦ Limits.prod.map f g)
+    (associator := prod.associator)
+    (leftUnitor := fun P ↦ prod.leftUnitor P)
+    (rightUnitor := fun P ↦ prod.rightUnitor P)
+    (pentagon := prod.pentagon)
+    (triangle := prod.triangle)
+    (associator_naturality := @prod.associator_naturality _ _ _)
 #align category_theory.monoidal_of_has_finite_products CategoryTheory.monoidalOfHasFiniteProducts
 
 end
 
-section
-
-attribute [local instance] monoidalOfHasFiniteProducts
-
-open MonoidalCategory
-
-/-- The monoidal structure coming from finite products is symmetric.
--/
-@[simps]
-def symmetricOfHasFiniteProducts [HasTerminal C] [HasBinaryProducts C] : SymmetricCategory C where
-  braiding X Y := Limits.prod.braiding X Y
-  braiding_naturality f g := by dsimp [tensorHom]; simp
-  hexagon_forward X Y Z := by dsimp [monoidalOfHasFiniteProducts]; simp
-  hexagon_reverse X Y Z := by dsimp [monoidalOfHasFiniteProducts]; simp
-  symmetry X Y := by dsimp; simp; rfl
-#align category_theory.symmetric_of_has_finite_products CategoryTheory.symmetricOfHasFiniteProducts
-
-end
-
 namespace monoidalOfHasFiniteProducts
 
 variable [HasTerminal C] [HasBinaryProducts C]
@@ -126,42 +108,47 @@ theorem associator_hom (X Y Z : C) :
   rfl
 #align category_theory.monoidal_of_has_finite_products.associator_hom CategoryTheory.monoidalOfHasFiniteProducts.associator_hom
 
-end monoidalOfHasFiniteProducts
-
-section
-
-/-- A category with an initial object and binary coproducts has a natural monoidal structure. -/
-def monoidalOfHasFiniteCoproducts [HasInitial C] [HasBinaryCoproducts C] : MonoidalCategory C where
-  tensorUnit' := ⊥_ C
-  tensorObj X Y := X ⨿ Y
-  tensorHom f g := Limits.coprod.map f g
-  associator := coprod.associator
-  leftUnitor := coprod.leftUnitor
-  rightUnitor := coprod.rightUnitor
-  pentagon := coprod.pentagon
-  triangle := coprod.triangle
-  associator_naturality := @coprod.associator_naturality _ _ _
-#align category_theory.monoidal_of_has_finite_coproducts CategoryTheory.monoidalOfHasFiniteCoproducts
+theorem associator_inv (X Y Z : C) :
+    (α_ X Y Z).inv =
+      prod.lift (prod.lift prod.fst (prod.snd ≫ prod.fst)) (prod.snd ≫ prod.snd) :=
+  rfl
 
-end
+end monoidalOfHasFiniteProducts
 
 section
 
-attribute [local instance] monoidalOfHasFiniteCoproducts
+attribute [local instance] monoidalOfHasFiniteProducts
 
 open MonoidalCategory
 
-/-- The monoidal structure coming from finite coproducts is symmetric.
+/-- The monoidal structure coming from finite products is symmetric.
 -/
 @[simps]
-def symmetricOfHasFiniteCoproducts [HasInitial C] [HasBinaryCoproducts C] :
-    SymmetricCategory C where
-  braiding := Limits.coprod.braiding
+def symmetricOfHasFiniteProducts [HasTerminal C] [HasBinaryProducts C] : SymmetricCategory C where
+  braiding X Y := Limits.prod.braiding X Y
   braiding_naturality f g := by dsimp [tensorHom]; simp
-  hexagon_forward X Y Z := by dsimp [monoidalOfHasFiniteCoproducts]; simp
-  hexagon_reverse X Y Z := by dsimp [monoidalOfHasFiniteCoproducts]; simp
-  symmetry X Y := by dsimp; simp; rfl
-#align category_theory.symmetric_of_has_finite_coproducts CategoryTheory.symmetricOfHasFiniteCoproducts
+  hexagon_forward X Y Z := by dsimp [monoidalOfHasFiniteProducts.associator_hom]; simp
+  hexagon_reverse X Y Z := by dsimp [monoidalOfHasFiniteProducts.associator_inv]; simp
+  symmetry X Y := by dsimp; simp
+#align category_theory.symmetric_of_has_finite_products CategoryTheory.symmetricOfHasFiniteProducts
+
+end
+
+section
+
+/-- A category with an initial object and binary coproducts has a natural monoidal structure. -/
+def monoidalOfHasFiniteCoproducts [HasInitial C] [HasBinaryCoproducts C] : MonoidalCategory C :=
+  .ofTensorHom
+    (tensorUnit' := ⊥_ C)
+    (tensorObj := fun X Y ↦ X ⨿ Y)
+    (tensorHom := fun f g ↦ Limits.coprod.map f g)
+    (associator := coprod.associator)
+    (leftUnitor := coprod.leftUnitor)
+    (rightUnitor := coprod.rightUnitor)
+    (pentagon := coprod.pentagon)
+    (triangle := coprod.triangle)
+    (associator_naturality := @coprod.associator_naturality _ _ _)
+#align category_theory.monoidal_of_has_finite_coproducts CategoryTheory.monoidalOfHasFiniteCoproducts
 
 end
 
@@ -212,6 +199,31 @@ theorem associator_hom (X Y Z : C) :
   rfl
 #align category_theory.monoidal_of_has_finite_coproducts.associator_hom CategoryTheory.monoidalOfHasFiniteCoproducts.associator_hom
 
+theorem associator_inv (X Y Z : C) :
+    (α_ X Y Z).inv =
+      coprod.desc (coprod.inl ≫ coprod.inl) (coprod.desc (coprod.inr ≫ coprod.inl) coprod.inr) :=
+  rfl
+
 end monoidalOfHasFiniteCoproducts
 
+section
+
+attribute [local instance] monoidalOfHasFiniteCoproducts
+
+open MonoidalCategory
+
+/-- The monoidal structure coming from finite coproducts is symmetric.
+-/
+@[simps]
+def symmetricOfHasFiniteCoproducts [HasInitial C] [HasBinaryCoproducts C] :
+    SymmetricCategory C where
+  braiding := Limits.coprod.braiding
+  braiding_naturality f g := by dsimp [tensorHom]; simp
+  hexagon_forward X Y Z := by dsimp [monoidalOfHasFiniteCoproducts.associator_hom]; simp
+  hexagon_reverse X Y Z := by dsimp [monoidalOfHasFiniteCoproducts.associator_inv]; simp
+  symmetry X Y := by dsimp; simp
+#align category_theory.symmetric_of_has_finite_coproducts CategoryTheory.symmetricOfHasFiniteCoproducts
+
+end
+
 end CategoryTheory

f153a85a

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

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Simon Hudon
-
-! This file was ported from Lean 3 source module category_theory.monoidal.of_has_finite_products
-! leanprover-community/mathlib commit f153a85a8dc0a96ce9133fed69e34df72f7f191f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Monoidal.Braided
 import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
 import Mathlib.CategoryTheory.Limits.Shapes.Terminal
 
+#align_import category_theory.monoidal.of_has_finite_products from "leanprover-community/mathlib"@"f153a85a8dc0a96ce9133fed69e34df72f7f191f"
+
 /-!
 # The natural monoidal structure on any category with finite (co)products.

f153a85a

chore: tidy various files (#5458)

2ac7bc89

Diff

@@ -25,12 +25,12 @@ and sometimes we want to think of a different monoidal structure entirely,
 we don't set up either construct as an instance.
 
 ## Implementation
-We had previously chosen to rely on `has_terminal` and `has_binary_products` instead of
-`has_finite_products`, because we were later relying on the definitional form of the tensor product.
+We had previously chosen to rely on `HasTerminal` and `HasBinaryProducts` instead of
+`HasBinaryProducts`, because we were later relying on the definitional form of the tensor product.
 Now that `has_limit` has been refactored to be a `Prop`,
 this issue is irrelevant and we could simplify the construction here.
 
-See `category_theory.monoidal.of_chosen_finite_products` for a variant of this construction
+See `CategoryTheory.monoidalOfChosenFiniteProducts` for a variant of this construction
 which allows specifying a particular choice of terminal object and binary products.
 -/
 
@@ -157,8 +157,8 @@ open MonoidalCategory
 /-- The monoidal structure coming from finite coproducts is symmetric.
 -/
 @[simps]
-def symmetricOfHasFiniteCoproducts [HasInitial C] [HasBinaryCoproducts C] : SymmetricCategory C
-    where
+def symmetricOfHasFiniteCoproducts [HasInitial C] [HasBinaryCoproducts C] :
+    SymmetricCategory C where
   braiding := Limits.coprod.braiding
   braiding_naturality f g := by dsimp [tensorHom]; simp
   hexagon_forward X Y Z := by dsimp [monoidalOfHasFiniteCoproducts]; simp

f153a85a

feat: port CategoryTheory.Monoidal.OfHasFiniteProducts (#4826)

Co-authored-by: Wojciech Nawrocki <wjnawrocki@protonmail.com>

d6a4e2fe

`category_theory.monoidal.of_has_finite_products` ⟷ `Mathlib.CategoryTheory.Monoidal.OfHasFiniteProducts`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 129

category_theory.monoidal.of_has_finite_products ⟷ Mathlib.CategoryTheory.Monoidal.OfHasFiniteProducts

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 129

`category_theory.monoidal.of_has_finite_products` ⟷ `Mathlib.CategoryTheory.Monoidal.OfHasFiniteProducts`