category_theory.products.basic | Mathlib porting status

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

dc6c365e

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

1ead2234

bump to nightly-2024-04-14-09

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

f736ea6b

Diff

@@ -204,8 +204,8 @@ def braiding : C × D ≌ D × C :=
 -/
 
 #print CategoryTheory.Prod.swapIsEquivalence /-
-instance swapIsEquivalence : IsEquivalence (swap C D) :=
-  (by infer_instance : IsEquivalence (braiding C D).Functor)
+instance swapIsEquivalence : CategoryTheory.Functor.IsEquivalence (swap C D) :=
+  (by infer_instance : CategoryTheory.Functor.IsEquivalence (braiding C D).Functor)
 #align category_theory.prod.swap_is_equivalence CategoryTheory.Prod.swapIsEquivalence
 -/

1ead2234

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -75,12 +75,12 @@ theorem isIso_prod_iff {P Q : C} {S T : D} {f : (P, S) ⟶ (Q, T)} :
     IsIso f ↔ IsIso f.1 ∧ IsIso f.2 := by
   constructor
   · rintro ⟨g, hfg, hgf⟩
-    simp at hfg hgf 
+    simp at hfg hgf
     rcases hfg with ⟨hfg₁, hfg₂⟩
     rcases hgf with ⟨hgf₁, hgf₂⟩
     exact ⟨⟨⟨g.1, hfg₁, hgf₁⟩⟩, ⟨⟨g.2, hfg₂, hgf₂⟩⟩⟩
   · rintro ⟨⟨g₁, hfg₁, hgf₁⟩, ⟨g₂, hfg₂, hgf₂⟩⟩
-    dsimp at hfg₁ hgf₁ hfg₂ hgf₂ 
+    dsimp at hfg₁ hgf₁ hfg₂ hgf₂
     refine' ⟨⟨(g₁, g₂), _, _⟩⟩ <;> · simp <;> constructor <;> assumption
 #align category_theory.is_iso_prod_iff CategoryTheory.isIso_prod_iff
 -/

1ead2234

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) 2017 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Stephen Morgan, Scott Morrison
 -/
-import Mathbin.CategoryTheory.EqToHom
-import Mathbin.CategoryTheory.Functor.Const
-import Mathbin.Data.Prod.Basic
+import CategoryTheory.EqToHom
+import CategoryTheory.Functor.Const
+import Data.Prod.Basic
 
 #align_import category_theory.products.basic from "leanprover-community/mathlib"@"1ead22342e1a078bd44744ace999f85756555d35"

1ead2234

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) 2017 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Stephen Morgan, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.products.basic
-! leanprover-community/mathlib commit 1ead22342e1a078bd44744ace999f85756555d35
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.EqToHom
 import Mathbin.CategoryTheory.Functor.Const
 import Mathbin.Data.Prod.Basic
 
+#align_import category_theory.products.basic from "leanprover-community/mathlib"@"1ead22342e1a078bd44744ace999f85756555d35"
+
 /-!
 # Cartesian products of categories

1ead2234

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -196,6 +196,7 @@ def symmetry : swap C D ⋙ swap D C ≅ 𝟭 (C × D)
 #align category_theory.prod.symmetry CategoryTheory.Prod.symmetry
 -/
 
+#print CategoryTheory.Prod.braiding /-
 /-- The equivalence, given by swapping factors, between `C × D` and `D × C`.
 -/
 @[simps]
@@ -203,6 +204,7 @@ def braiding : C × D ≌ D × C :=
   Equivalence.mk (swap C D) (swap D C) (NatIso.ofComponents (fun X => eqToIso (by simp)) (by tidy))
     (NatIso.ofComponents (fun X => eqToIso (by simp)) (by tidy))
 #align category_theory.prod.braiding CategoryTheory.Prod.braiding
+-/
 
 #print CategoryTheory.Prod.swapIsEquivalence /-
 instance swapIsEquivalence : IsEquivalence (swap C D) :=
@@ -252,11 +254,13 @@ def evaluationUncurried : C × (C ⥤ D) ⥤ D
 
 variable {C}
 
+#print CategoryTheory.Functor.constCompEvaluationObj /-
 /-- The constant functor followed by the evalutation functor is just the identity. -/
 @[simps]
 def Functor.constCompEvaluationObj (X : C) : Functor.const C ⋙ (evaluation C D).obj X ≅ 𝟭 D :=
   NatIso.ofComponents (fun Y => Iso.refl _) fun Y Z f => by simp
 #align category_theory.functor.const_comp_evaluation_obj CategoryTheory.Functor.constCompEvaluationObj
+-/
 
 end
 
@@ -314,15 +318,19 @@ def diag : C ⥤ C × C :=
 #align category_theory.functor.diag CategoryTheory.Functor.diag
 -/
 
+#print CategoryTheory.Functor.diag_obj /-
 @[simp]
 theorem diag_obj (X : C) : (diag C).obj X = (X, X) :=
   rfl
 #align category_theory.functor.diag_obj CategoryTheory.Functor.diag_obj
+-/
 
+#print CategoryTheory.Functor.diag_map /-
 @[simp]
 theorem diag_map {X Y : C} (f : X ⟶ Y) : (diag C).map f = (f, f) :=
   rfl
 #align category_theory.functor.diag_map CategoryTheory.Functor.diag_map
+-/
 
 end
 
@@ -347,11 +355,13 @@ def prod {F G : A ⥤ B} {H I : C ⥤ D} (α : F ⟶ G) (β : H ⟶ I) : F.Prod
    use instead `α.prod β` or `nat_trans.prod α β`. -/
 end NatTrans
 
+#print CategoryTheory.flipCompEvaluation /-
 /-- `F.flip` composed with evaluation is the same as evaluating `F`. -/
 @[simps]
 def flipCompEvaluation (F : A ⥤ B ⥤ C) (a) : F.flip ⋙ (evaluation _ _).obj a ≅ F.obj a :=
   (NatIso.ofComponents fun b => eqToIso rfl) <| by tidy
 #align category_theory.flip_comp_evaluation CategoryTheory.flipCompEvaluation
+-/
 
 variable (A B C)
 
@@ -403,6 +413,7 @@ def functorProdFunctorEquivCounitIso :
 #align category_theory.functor_prod_functor_equiv_counit_iso CategoryTheory.functorProdFunctorEquivCounitIso
 -/
 
+#print CategoryTheory.functorProdFunctorEquiv /-
 /-- The equivalence of categories between `(A ⥤ B) × (A ⥤ C)` and `A ⥤ (B × C)` -/
 @[simps]
 def functorProdFunctorEquiv : (A ⥤ B) × (A ⥤ C) ≌ A ⥤ B × C
@@ -412,6 +423,7 @@ def functorProdFunctorEquiv : (A ⥤ B) × (A ⥤ C) ≌ A ⥤ B × C
   unitIso := functorProdFunctorEquivUnitIso A B C
   counitIso := functorProdFunctorEquivCounitIso A B C
 #align category_theory.functor_prod_functor_equiv CategoryTheory.functorProdFunctorEquiv
+-/
 
 end CategoryTheory

1ead2234

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -78,12 +78,12 @@ theorem isIso_prod_iff {P Q : C} {S T : D} {f : (P, S) ⟶ (Q, T)} :
     IsIso f ↔ IsIso f.1 ∧ IsIso f.2 := by
   constructor
   · rintro ⟨g, hfg, hgf⟩
-    simp at hfg hgf
+    simp at hfg hgf 
     rcases hfg with ⟨hfg₁, hfg₂⟩
     rcases hgf with ⟨hgf₁, hgf₂⟩
     exact ⟨⟨⟨g.1, hfg₁, hgf₁⟩⟩, ⟨⟨g.2, hfg₂, hgf₂⟩⟩⟩
   · rintro ⟨⟨g₁, hfg₁, hgf₁⟩, ⟨g₂, hfg₂, hgf₂⟩⟩
-    dsimp at hfg₁ hgf₁ hfg₂ hgf₂
+    dsimp at hfg₁ hgf₁ hfg₂ hgf₂ 
     refine' ⟨⟨(g₁, g₂), _, _⟩⟩ <;> · simp <;> constructor <;> assumption
 #align category_theory.is_iso_prod_iff CategoryTheory.isIso_prod_iff
 -/

1ead2234

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -196,12 +196,6 @@ def symmetry : swap C D ⋙ swap D C ≅ 𝟭 (C × D)
 #align category_theory.prod.symmetry CategoryTheory.Prod.symmetry
 -/
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.prod.braiding CategoryTheory.Prod.braidingₓ'. -/
 /-- The equivalence, given by swapping factors, between `C × D` and `D × C`.
 -/
 @[simps]
@@ -258,12 +252,6 @@ def evaluationUncurried : C × (C ⥤ D) ⥤ D
 
 variable {C}
 
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 /-- The constant functor followed by the evalutation functor is just the identity. -/
 @[simps]
 def Functor.constCompEvaluationObj (X : C) : Functor.const C ⋙ (evaluation C D).obj X ≅ 𝟭 D :=
@@ -326,23 +314,11 @@ def diag : C ⥤ C × C :=
 #align category_theory.functor.diag CategoryTheory.Functor.diag
 -/
 
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 @[simp]
 theorem diag_obj (X : C) : (diag C).obj X = (X, X) :=
   rfl
 #align category_theory.functor.diag_obj CategoryTheory.Functor.diag_obj
 
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 @[simp]
 theorem diag_map {X Y : C} (f : X ⟶ Y) : (diag C).map f = (f, f) :=
   rfl
@@ -371,12 +347,6 @@ def prod {F G : A ⥤ B} {H I : C ⥤ D} (α : F ⟶ G) (β : H ⟶ I) : F.Prod
    use instead `α.prod β` or `nat_trans.prod α β`. -/
 end NatTrans
 
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 /-- `F.flip` composed with evaluation is the same as evaluating `F`. -/
 @[simps]
 def flipCompEvaluation (F : A ⥤ B ⥤ C) (a) : F.flip ⋙ (evaluation _ _).obj a ≅ F.obj a :=
@@ -433,12 +403,6 @@ def functorProdFunctorEquivCounitIso :
 #align category_theory.functor_prod_functor_equiv_counit_iso CategoryTheory.functorProdFunctorEquivCounitIso
 -/
 
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 /-- The equivalence of categories between `(A ⥤ B) × (A ⥤ C)` and `A ⥤ (B × C)` -/
 @[simps]
 def functorProdFunctorEquiv : (A ⥤ B) × (A ⥤ C) ≌ A ⥤ B × C

1ead2234

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

dc6c365e

chore(CategoryTheory): move Full, Faithful, EssSurj, IsEquivalence and ReflectsIsomorphisms to the Functor namespace (#11985)

These notions on functors are now Functor.Full, Functor.Faithful, Functor.EssSurj, Functor.IsEquivalence, Functor.ReflectsIsomorphisms. Deprecated aliases are introduced for the previous names.

65b7affc

Diff

@@ -175,8 +175,8 @@ def braiding : C × D ≌ D × C :=
     (NatIso.ofComponents fun X => eqToIso (by simp))
 #align category_theory.prod.braiding CategoryTheory.Prod.braiding
 
-instance swapIsEquivalence : IsEquivalence (swap C D) :=
-  (by infer_instance : IsEquivalence (braiding C D).functor)
+instance swapIsEquivalence : (swap C D).IsEquivalence :=
+  (by infer_instance : (braiding C D).functor.IsEquivalence)
 #align category_theory.prod.swap_is_equivalence CategoryTheory.Prod.swapIsEquivalence
 
 end Prod

dc6c365e

chore: replace remaining lambda syntax (#11405)

Includes some doc comments and real code: this is exhaustive, with two exceptions:

some files are handled in #11409 instead
I left FunProp/{ToStd,RefinedDiscTree}.lean, Tactic/NormNum and Tactic/Simps alone, as these seem likely enough to end up in std.

Follow-up to #11301, much shorter this time.

f0f609c6

Diff

@@ -384,11 +384,11 @@ open Opposite
 @[simps]
 def prodOpEquiv : (C × D)ᵒᵖ ≌ Cᵒᵖ × Dᵒᵖ where
   functor :=
-    { obj := λ X => ⟨op X.unop.1, op X.unop.2⟩,
-      map := λ f => ⟨f.unop.1.op, f.unop.2.op⟩ }
+    { obj := fun X ↦ ⟨op X.unop.1, op X.unop.2⟩,
+      map := fun f ↦ ⟨f.unop.1.op, f.unop.2.op⟩ }
   inverse :=
-    { obj := λ ⟨X,Y⟩ => op ⟨X.unop, Y.unop⟩,
-      map := λ ⟨f,g⟩ => op ⟨f.unop, g.unop⟩ }
+    { obj := fun ⟨X,Y⟩ ↦ op ⟨X.unop, Y.unop⟩,
+      map := fun ⟨f,g⟩ ↦ op ⟨f.unop, g.unop⟩ }
   unitIso := Iso.refl _
   counitIso := Iso.refl _
   functor_unitIso_comp := fun ⟨X, Y⟩ => by

dc6c365e

chore: move Mathlib to v4.7.0-rc1 (#11162)

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

fa48894a

Diff

@@ -393,7 +393,7 @@ def prodOpEquiv : (C × D)ᵒᵖ ≌ Cᵒᵖ × Dᵒᵖ where
   counitIso := Iso.refl _
   functor_unitIso_comp := fun ⟨X, Y⟩ => by
     dsimp
-    ext <;> simpa using Category.id_comp _
+    ext <;> apply Category.id_comp
 
 end Opposite

dc6c365e

chore: Remove nonterminal simp at (#7795)

Removes nonterminal uses of simp at. Replaces most of these with instances of simp? ... says.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

4160b2aa

Diff

@@ -66,7 +66,7 @@ theorem isIso_prod_iff {P Q : C} {S T : D} {f : (P, S) ⟶ (Q, T)} :
     IsIso f ↔ IsIso f.1 ∧ IsIso f.2 := by
   constructor
   · rintro ⟨g, hfg, hgf⟩
-    simp at hfg hgf
+    simp? at hfg hgf says simp only [prod_Hom, prod_comp, prod_id, Prod.mk.injEq] at hfg hgf
     rcases hfg with ⟨hfg₁, hfg₂⟩
     rcases hgf with ⟨hgf₁, hgf₂⟩
     exact ⟨⟨⟨g.1, hfg₁, hgf₁⟩⟩, ⟨⟨g.2, hfg₂, hgf₂⟩⟩⟩

dc6c365e

feat(CategoryTheory): the localized category of a product category (#8516)

This PR develops the API for cartesian products of categories (natural isomorphisms, equivalences, morphism properties) in order to show that under simple assumptions, the localized category of a product of two categories identifies to a product of the localized categories.

2bfea869

Diff

@@ -298,6 +298,29 @@ def prod {F G : A ⥤ B} {H I : C ⥤ D} (α : F ⟶ G) (β : H ⟶ I) : F.prod
    use instead `α.prod β` or `NatTrans.prod α β`. -/
 end NatTrans
 
+namespace NatIso
+
+/-- The cartesian product of two natural isomorphisms. -/
+@[simps]
+def prod {F F' : A ⥤ B} {G G' : C ⥤ D} (e₁ : F ≅ F') (e₂ : G ≅ G') :
+    F.prod G ≅ F'.prod G' where
+  hom := NatTrans.prod e₁.hom e₂.hom
+  inv := NatTrans.prod e₁.inv e₂.inv
+
+end NatIso
+
+namespace Equivalence
+
+/-- The cartesian product of two equivalences of categories. -/
+@[simps]
+def prod (E₁ : A ≌ B) (E₂ : C ≌ D) : A × C ≌ B × D where
+  functor := E₁.functor.prod E₂.functor
+  inverse := E₁.inverse.prod E₂.inverse
+  unitIso := NatIso.prod E₁.unitIso E₂.unitIso
+  counitIso := NatIso.prod E₁.counitIso E₂.counitIso
+
+end Equivalence
+
 /-- `F.flip` composed with evaluation is the same as evaluating `F`. -/
 @[simps!]
 def flipCompEvaluation (F : A ⥤ B ⥤ C) (a) : F.flip ⋙ (evaluation _ _).obj a ≅ F.obj a :=

dc6c365e

feat(CategoryTheory/Products): opposite of product of categories (#8150)

Equivalence between the opposite of a product of categories and the product of the opposites.

5ed5d163

Diff

@@ -5,6 +5,7 @@ Authors: Stephen Morgan, Scott Morrison
 -/
 import Mathlib.CategoryTheory.EqToHom
 import Mathlib.CategoryTheory.Functor.Const
+import Mathlib.CategoryTheory.Opposites
 import Mathlib.Data.Prod.Basic
 
 #align_import category_theory.products.basic from "leanprover-community/mathlib"@"dc6c365e751e34d100e80fe6e314c3c3e0fd2988"
@@ -352,4 +353,25 @@ def functorProdFunctorEquiv : (A ⥤ B) × (A ⥤ C) ≌ A ⥤ B × C :=
     counitIso := functorProdFunctorEquivCounitIso A B C, }
 #align category_theory.functor_prod_functor_equiv CategoryTheory.functorProdFunctorEquiv
 
+section Opposite
+
+open Opposite
+
+/-- The equivalence between the opposite of a product and the product of the opposites. -/
+@[simps]
+def prodOpEquiv : (C × D)ᵒᵖ ≌ Cᵒᵖ × Dᵒᵖ where
+  functor :=
+    { obj := λ X => ⟨op X.unop.1, op X.unop.2⟩,
+      map := λ f => ⟨f.unop.1.op, f.unop.2.op⟩ }
+  inverse :=
+    { obj := λ ⟨X,Y⟩ => op ⟨X.unop, Y.unop⟩,
+      map := λ ⟨f,g⟩ => op ⟨f.unop, g.unop⟩ }
+  unitIso := Iso.refl _
+  counitIso := Iso.refl _
+  functor_unitIso_comp := fun ⟨X, Y⟩ => by
+    dsimp
+    ext <;> simpa using Category.id_comp _
+
+end Opposite
+
 end CategoryTheory

dc6c365e

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) 2017 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Stephen Morgan, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.products.basic
-! leanprover-community/mathlib commit dc6c365e751e34d100e80fe6e314c3c3e0fd2988
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.EqToHom
 import Mathlib.CategoryTheory.Functor.Const
 import Mathlib.Data.Prod.Basic
 
+#align_import category_theory.products.basic from "leanprover-community/mathlib"@"dc6c365e751e34d100e80fe6e314c3c3e0fd2988"
+
 /-!
 # Cartesian products of categories

dc6c365e

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -158,7 +158,7 @@ def swap : C × D ⥤ D × C where
   map f := (f.2, f.1)
 #align category_theory.prod.swap CategoryTheory.Prod.swap
 
-/-- Swapping the factors of a cartesion product of categories twice is naturally isomorphic
+/-- Swapping the factors of a cartesian product of categories twice is naturally isomorphic
 to the identity functor.
 -/
 @[simps]

dc6c365e

chore: review of automation in category theory (#4793)

Clean up of automation in the category theory library. Leaving out unnecessary proof steps, or fields done by aesop_cat, and making more use of available autoparameters.

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

5b958613

Diff

@@ -173,8 +173,8 @@ def symmetry : swap C D ⋙ swap D C ≅ 𝟭 (C × D)
 @[simps!]
 def braiding : C × D ≌ D × C :=
   Equivalence.mk (swap C D) (swap D C)
-    (NatIso.ofComponents (fun X => eqToIso (by simp)) (by aesop_cat))
-    (NatIso.ofComponents (fun X => eqToIso (by simp)) (by aesop_cat))
+    (NatIso.ofComponents fun X => eqToIso (by simp))
+    (NatIso.ofComponents fun X => eqToIso (by simp))
 #align category_theory.prod.braiding CategoryTheory.Prod.braiding
 
 instance swapIsEquivalence : IsEquivalence (swap C D) :=
@@ -192,8 +192,7 @@ variable (C : Type u₁) [Category.{v₁} C] (D : Type u₂) [Category.{v₂} D]
 which is functorial in both `X` and `F`.
 -/
 @[simps]
-def evaluation : C ⥤ (C ⥤ D) ⥤ D
-    where
+def evaluation : C ⥤ (C ⥤ D) ⥤ D where
   obj X :=
     { obj := fun F => F.obj X
       map := fun α => α.app X }
@@ -206,8 +205,7 @@ def evaluation : C ⥤ (C ⥤ D) ⥤ D
 as a functor `C × (C ⥤ D) ⥤ D`.
 -/
 @[simps]
-def evaluationUncurried : C × (C ⥤ D) ⥤ D
-    where
+def evaluationUncurried : C × (C ⥤ D) ⥤ D where
   obj p := p.2.obj p.1
   map := fun {x} {y} f => x.2.map f.1 ≫ f.2.app y.1
   map_comp := fun {X} {Y} {Z} f g => by
@@ -222,7 +220,7 @@ variable {C}
 /-- The constant functor followed by the evaluation functor is just the identity. -/
 @[simps!]
 def Functor.constCompEvaluationObj (X : C) : Functor.const C ⋙ (evaluation C D).obj X ≅ 𝟭 D :=
-  NatIso.ofComponents (fun Y => Iso.refl _) fun {Y} {Z} f => by simp
+  NatIso.ofComponents fun Y => Iso.refl _
 #align category_theory.functor.const_comp_evaluation_obj CategoryTheory.Functor.constCompEvaluationObj
 
 end
@@ -234,8 +232,7 @@ namespace Functor
 
 /-- The cartesian product of two functors. -/
 @[simps]
-def prod (F : A ⥤ B) (G : C ⥤ D) : A × C ⥤ B × D
-    where
+def prod (F : A ⥤ B) (G : C ⥤ D) : A × C ⥤ B × D where
   obj X := (F.obj X.1, G.obj X.2)
   map f := (F.map f.1, G.map f.2)
 #align category_theory.functor.prod CategoryTheory.Functor.prod
@@ -244,8 +241,7 @@ def prod (F : A ⥤ B) (G : C ⥤ D) : A × C ⥤ B × D
    You can use `F.prod G` as a "poor man's infix", or just write `functor.prod F G`. -/
 /-- Similar to `prod`, but both functors start from the same category `A` -/
 @[simps]
-def prod' (F : A ⥤ B) (G : A ⥤ C) : A ⥤ B × C
-    where
+def prod' (F : A ⥤ B) (G : A ⥤ C) : A ⥤ B × C where
   obj a := (F.obj a, G.obj a)
   map f := (F.map f, G.map f)
 #align category_theory.functor.prod' CategoryTheory.Functor.prod'
@@ -253,13 +249,13 @@ def prod' (F : A ⥤ B) (G : A ⥤ C) : A ⥤ B × C
 /-- The product `F.prod' G` followed by projection on the first component is isomorphic to `F` -/
 @[simps!]
 def prod'CompFst (F : A ⥤ B) (G : A ⥤ C) : F.prod' G ⋙ CategoryTheory.Prod.fst B C ≅ F :=
-  NatIso.ofComponents (fun X => Iso.refl _) fun f => by simp
+  NatIso.ofComponents fun X => Iso.refl _
 #align category_theory.functor.prod'_comp_fst CategoryTheory.Functor.prod'CompFst
 
 /-- The product `F.prod' G` followed by projection on the second component is isomorphic to `G` -/
 @[simps!]
 def prod'CompSnd (F : A ⥤ B) (G : A ⥤ C) : F.prod' G ⋙ CategoryTheory.Prod.snd B C ≅ G :=
-  NatIso.ofComponents (fun X => Iso.refl _) fun f => by simp
+  NatIso.ofComponents fun X => Iso.refl _
 #align category_theory.functor.prod'_comp_snd CategoryTheory.Functor.prod'CompSnd
 
 section
@@ -307,7 +303,7 @@ end NatTrans
 /-- `F.flip` composed with evaluation is the same as evaluating `F`. -/
 @[simps!]
 def flipCompEvaluation (F : A ⥤ B ⥤ C) (a) : F.flip ⋙ (evaluation _ _).obj a ≅ F.obj a :=
-  (NatIso.ofComponents fun b => eqToIso rfl) <| by aesop_cat
+  NatIso.ofComponents fun b => eqToIso rfl
 #align category_theory.flip_comp_evaluation CategoryTheory.flipCompEvaluation
 
 variable (A B C)
@@ -338,36 +334,25 @@ def functorProdToProdFunctor : (A ⥤ B × C) ⥤ (A ⥤ B) × (A ⥤ C)
 @[simps!]
 def functorProdFunctorEquivUnitIso :
     𝟭 _ ≅ prodFunctorToFunctorProd A B C ⋙ functorProdToProdFunctor A B C :=
-  NatIso.ofComponents
-    (fun F =>
-      (((Functor.prod'CompFst F.fst F.snd).prod (Functor.prod'CompSnd F.fst F.snd)).trans
-        (prod.etaIso F)).symm)
-      (fun α => by aesop_cat)
+  NatIso.ofComponents fun F =>
+    (((Functor.prod'CompFst F.fst F.snd).prod (Functor.prod'CompSnd F.fst F.snd)).trans
+      (prod.etaIso F)).symm
 #align category_theory.functor_prod_functor_equiv_unit_iso CategoryTheory.functorProdFunctorEquivUnitIso
 
 /-- The counit isomorphism for `functorProdFunctorEquiv` -/
 @[simps!]
 def functorProdFunctorEquivCounitIso :
     functorProdToProdFunctor A B C ⋙ prodFunctorToFunctorProd A B C ≅ 𝟭 _ :=
-  NatIso.ofComponents (fun F => NatIso.ofComponents (fun X => prod.etaIso (F.obj X)) (by aesop_cat))
-    (by aesop_cat)
+  NatIso.ofComponents fun F => NatIso.ofComponents fun X => prod.etaIso (F.obj X)
 #align category_theory.functor_prod_functor_equiv_counit_iso CategoryTheory.functorProdFunctorEquivCounitIso
 
-/- Porting note: unlike with Lean 3, we needed to provide `functor_unitIso_comp` because
-Lean 4 could not see through `functorProdFunctorEquivUnitIso` (or the co-unit version)
-to run the auto tactic `by aesop_cat` -/
-
 /-- The equivalence of categories between `(A ⥤ B) × (A ⥤ C)` and `A ⥤ (B × C)` -/
 @[simps]
 def functorProdFunctorEquiv : (A ⥤ B) × (A ⥤ C) ≌ A ⥤ B × C :=
   { functor := prodFunctorToFunctorProd A B C,
     inverse := functorProdToProdFunctor A B C,
     unitIso := functorProdFunctorEquivUnitIso A B C,
-    counitIso := functorProdFunctorEquivCounitIso A B C,
-    functor_unitIso_comp := by
-      simp only [functorProdFunctorEquivUnitIso]
-      aesop_cat
-  }
+    counitIso := functorProdFunctorEquivCounitIso A B C, }
 #align category_theory.functor_prod_functor_equiv CategoryTheory.functorProdFunctorEquiv
 
 end CategoryTheory

dc6c365e

chore: fix typos (#4518)

I ran codespell Mathlib and got tired halfway through the suggestions.

92beef58

Diff

@@ -219,7 +219,7 @@ def evaluationUncurried : C × (C ⥤ D) ⥤ D
 
 variable {C}
 
-/-- The constant functor followed by the evalutation functor is just the identity. -/
+/-- The constant functor followed by the evaluation functor is just the identity. -/
 @[simps!]
 def Functor.constCompEvaluationObj (X : C) : Functor.const C ⋙ (evaluation C D).obj X ≅ 𝟭 D :=
   NatIso.ofComponents (fun Y => Iso.refl _) fun {Y} {Z} f => by simp

dc6c365e

chore: forward port of #18742, no simps lemmas for Category.Hom (#3340)

This is the forward port of https://github.com/leanprover-community/mathlib/pull/18742. That PR hasn't landed yet, so this PR still needs to be updated with the new commit SHA.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>

e44913f3

Diff

@@ -44,7 +44,7 @@ variable (C : Type u₁) [Category.{v₁} C] (D : Type u₂) [Category.{v₂} D]
 
 See <https://stacks.math.columbia.edu/tag/001K>.
 -/
-@[simps (config := { notRecursive := [] })]
+@[simps (config := { notRecursive := [] }) Hom id_fst id_snd comp_fst comp_snd]
 instance prod : Category.{max v₁ v₂} (C × D)
     where
   Hom X Y := (X.1 ⟶ Y.1) × (X.2 ⟶ Y.2)

dc6c365e

chore: strip trailing spaces in lean files (#2828)

vscode is already configured by .vscode/settings.json to trim these on save. It's not clear how they've managed to stick around.

By doing this all in one PR now, it avoids getting random whitespace diffs in PRs later.

This was done with a regex search in vscode,

6ceb5945

Diff

@@ -172,7 +172,7 @@ def symmetry : swap C D ⋙ swap D C ≅ 𝟭 (C × D)
 -/
 @[simps!]
 def braiding : C × D ≌ D × C :=
-  Equivalence.mk (swap C D) (swap D C) 
+  Equivalence.mk (swap C D) (swap D C)
     (NatIso.ofComponents (fun X => eqToIso (by simp)) (by aesop_cat))
     (NatIso.ofComponents (fun X => eqToIso (by simp)) (by aesop_cat))
 #align category_theory.prod.braiding CategoryTheory.Prod.braiding
@@ -294,9 +294,9 @@ def prod {F G : A ⥤ B} {H I : C ⥤ D} (α : F ⟶ G) (β : H ⟶ I) : F.prod
   app X := (α.app X.1, β.app X.2)
   naturality {X} {Y} f := by
     cases X; cases Y
-    simp only [Functor.prod_map, prod_comp] 
-    rw [Prod.mk.inj_iff] 
-    constructor 
+    simp only [Functor.prod_map, prod_comp]
+    rw [Prod.mk.inj_iff]
+    constructor
     repeat {rw [naturality]}
 #align category_theory.nat_trans.prod CategoryTheory.NatTrans.prod
 
@@ -338,11 +338,11 @@ def functorProdToProdFunctor : (A ⥤ B × C) ⥤ (A ⥤ B) × (A ⥤ C)
 @[simps!]
 def functorProdFunctorEquivUnitIso :
     𝟭 _ ≅ prodFunctorToFunctorProd A B C ⋙ functorProdToProdFunctor A B C :=
-  NatIso.ofComponents 
-    (fun F => 
-      (((Functor.prod'CompFst F.fst F.snd).prod (Functor.prod'CompSnd F.fst F.snd)).trans 
-        (prod.etaIso F)).symm) 
-      (fun α => by aesop_cat) 
+  NatIso.ofComponents
+    (fun F =>
+      (((Functor.prod'CompFst F.fst F.snd).prod (Functor.prod'CompSnd F.fst F.snd)).trans
+        (prod.etaIso F)).symm)
+      (fun α => by aesop_cat)
 #align category_theory.functor_prod_functor_equiv_unit_iso CategoryTheory.functorProdFunctorEquivUnitIso
 
 /-- The counit isomorphism for `functorProdFunctorEquiv` -/
@@ -354,12 +354,12 @@ def functorProdFunctorEquivCounitIso :
 #align category_theory.functor_prod_functor_equiv_counit_iso CategoryTheory.functorProdFunctorEquivCounitIso
 
 /- Porting note: unlike with Lean 3, we needed to provide `functor_unitIso_comp` because
-Lean 4 could not see through `functorProdFunctorEquivUnitIso` (or the co-unit version) 
+Lean 4 could not see through `functorProdFunctorEquivUnitIso` (or the co-unit version)
 to run the auto tactic `by aesop_cat` -/
 
 /-- The equivalence of categories between `(A ⥤ B) × (A ⥤ C)` and `A ⥤ (B × C)` -/
 @[simps]
-def functorProdFunctorEquiv : (A ⥤ B) × (A ⥤ C) ≌ A ⥤ B × C := 
+def functorProdFunctorEquiv : (A ⥤ B) × (A ⥤ C) ≌ A ⥤ B × C :=
   { functor := prodFunctorToFunctorProd A B C,
     inverse := functorProdToProdFunctor A B C,
     unitIso := functorProdFunctorEquivUnitIso A B C,

dc6c365e

fix: rename functor_unit_iso_comp to functor_unitIso_comp (#2314)

3d04ae46

Diff

@@ -353,7 +353,7 @@ def functorProdFunctorEquivCounitIso :
     (by aesop_cat)
 #align category_theory.functor_prod_functor_equiv_counit_iso CategoryTheory.functorProdFunctorEquivCounitIso
 
-/- Porting note: unlike with Lean 3, we needed to provide `functor_unit_iso_comp` because 
+/- Porting note: unlike with Lean 3, we needed to provide `functor_unitIso_comp` because
 Lean 4 could not see through `functorProdFunctorEquivUnitIso` (or the co-unit version) 
 to run the auto tactic `by aesop_cat` -/
 
@@ -364,7 +364,7 @@ def functorProdFunctorEquiv : (A ⥤ B) × (A ⥤ C) ≌ A ⥤ B × C :=
     inverse := functorProdToProdFunctor A B C,
     unitIso := functorProdFunctorEquivUnitIso A B C,
     counitIso := functorProdFunctorEquivCounitIso A B C,
-    functor_unit_iso_comp := by
+    functor_unitIso_comp := by
       simp only [functorProdFunctorEquivUnitIso]
       aesop_cat
   }

dc6c365e

feat port/CategoryTheory.Products.Basic (#2211)

e6816f7d

`category_theory.products.basic` ⟷ `Mathlib.CategoryTheory.Products.Basic`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 14

category_theory.products.basic ⟷ Mathlib.CategoryTheory.Products.Basic

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 14

`category_theory.products.basic` ⟷ `Mathlib.CategoryTheory.Products.Basic`