category_theory.monoidal.internal.types ⟷ Mathlib.CategoryTheory.Monoidal.Internal.Types

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Algebra.Category.Mon.Basic
+import Algebra.Category.MonCat.Basic
 import CategoryTheory.Monoidal.CommMon_
 import CategoryTheory.Monoidal.Types.Symmetric
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.Algebra.Category.Mon.Basic
-import Mathbin.CategoryTheory.Monoidal.CommMon_
-import Mathbin.CategoryTheory.Monoidal.Types.Symmetric
+import Algebra.Category.Mon.Basic
+import CategoryTheory.Monoidal.CommMon_
+import CategoryTheory.Monoidal.Types.Symmetric
 
 #align_import category_theory.monoidal.internal.types from "leanprover-community/mathlib"@"f2ad3645af9effcdb587637dc28a6074edc813f9"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -143,7 +143,7 @@ def inverse : CommMonCat.{u} ⥤ CommMon_ (Type u)
     where
   obj A :=
     { MonTypeEquivalenceMon.inverse.obj ((forget₂ CommMonCat MonCat).obj A) with
-      mul_comm' := by ext ⟨x, y⟩; exact CommMonoid.mul_comm y x }
+      mul_comm' := by ext ⟨x, y⟩; exact CommMonoid.hMul_comm y x }
   map A B f := MonTypeEquivalenceMon.inverse.map f
 #align CommMon_Type_equivalence_CommMon.inverse CommMonTypeEquivalenceCommMon.inverse
 -/

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.monoidal.internal.types
-! leanprover-community/mathlib commit f2ad3645af9effcdb587637dc28a6074edc813f9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Category.Mon.Basic
 import Mathbin.CategoryTheory.Monoidal.CommMon_
 import Mathbin.CategoryTheory.Monoidal.Types.Symmetric
 
+#align_import category_theory.monoidal.internal.types from "leanprover-community/mathlib"@"f2ad3645af9effcdb587637dc28a6074edc813f9"
+
 /-!
 # `Mon_ (Type u) ≌ Mon.{u}`
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/f2ad3645af9effcdb587637dc28a6074edc813f9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module category_theory.monoidal.internal.types
-! leanprover-community/mathlib commit 95a87616d63b3cb49d3fe678d416fbe9c4217bf4
+! leanprover-community/mathlib commit f2ad3645af9effcdb587637dc28a6074edc813f9
 ! 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.Monoidal.Types.Symmetric
 /-!
 # `Mon_ (Type u) ≌ Mon.{u}`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The category of internal monoid objects in `Type`
 is equivalent to the category of "native" bundled monoids.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -28,6 +28,7 @@ open CategoryTheory
 
 namespace monTypeEquivalenceMon
 
+#print MonTypeEquivalenceMon.monMonoid /-
 instance monMonoid (A : Mon_ (Type u)) : Monoid A.pt
     where
   one := A.one PUnit.unit
@@ -36,7 +37,9 @@ instance monMonoid (A : Mon_ (Type u)) : Monoid A.pt
   mul_one x := by convert congr_fun A.mul_one (x, PUnit.unit)
   mul_assoc x y z := by convert congr_fun A.mul_assoc ((x, y), z)
 #align Mon_Type_equivalence_Mon.Mon_monoid MonTypeEquivalenceMon.monMonoid
+-/
 
+#print MonTypeEquivalenceMon.functor /-
 /-- Converting a monoid object in `Type` to a bundled monoid.
 -/
 def functor : Mon_ (Type u) ⥤ MonCat.{u}
@@ -47,7 +50,9 @@ def functor : Mon_ (Type u) ⥤ MonCat.{u}
       map_one' := congr_fun f.OneHom PUnit.unit
       map_mul' := fun x y => congr_fun f.MulHom (x, y) }
 #align Mon_Type_equivalence_Mon.functor MonTypeEquivalenceMon.functor
+-/
 
+#print MonTypeEquivalenceMon.inverse /-
 /-- Converting a bundled monoid to a monoid object in `Type`.
 -/
 def inverse : MonCat.{u} ⥤ Mon_ (Type u)
@@ -61,11 +66,13 @@ def inverse : MonCat.{u} ⥤ Mon_ (Type u)
       mul_assoc' := by ext ⟨⟨x, y⟩, z⟩; simp [mul_assoc] }
   map A B f := { Hom := f }
 #align Mon_Type_equivalence_Mon.inverse MonTypeEquivalenceMon.inverse
+-/
 
 end monTypeEquivalenceMon
 
 open monTypeEquivalenceMon
 
+#print monTypeEquivalenceMon /-
 /-- The category of internal monoid objects in `Type`
 is equivalent to the category of "native" bundled monoids.
 -/
@@ -92,7 +99,9 @@ def monTypeEquivalenceMon : Mon_ (Type u) ≌ MonCat.{u}
               map_mul' := fun x y => rfl } })
       (by tidy)
 #align Mon_Type_equivalence_Mon monTypeEquivalenceMon
+-/
 
+#print monTypeEquivalenceMonForget /-
 /-- The equivalence `Mon_ (Type u) ≌ Mon.{u}`
 is naturally compatible with the forgetful functors to `Type u`.
 -/
@@ -100,18 +109,24 @@ def monTypeEquivalenceMonForget :
     MonTypeEquivalenceMon.functor ⋙ forget MonCat ≅ Mon_.forget (Type u) :=
   NatIso.ofComponents (fun A => Iso.refl _) (by tidy)
 #align Mon_Type_equivalence_Mon_forget monTypeEquivalenceMonForget
+-/
 
+#print monTypeInhabited /-
 instance monTypeInhabited : Inhabited (Mon_ (Type u)) :=
   ⟨MonTypeEquivalenceMon.inverse.obj (MonCat.of PUnit)⟩
 #align Mon_Type_inhabited monTypeInhabited
+-/
 
 namespace commMonTypeEquivalenceCommMon
 
+#print CommMonTypeEquivalenceCommMon.commMonCommMonoid /-
 instance commMonCommMonoid (A : CommMon_ (Type u)) : CommMonoid A.pt :=
   { MonTypeEquivalenceMon.monMonoid A.toMon_ with
     mul_comm := fun x y => by convert congr_fun A.mul_comm (y, x) }
 #align CommMon_Type_equivalence_CommMon.CommMon_comm_monoid CommMonTypeEquivalenceCommMon.commMonCommMonoid
+-/
 
+#print CommMonTypeEquivalenceCommMon.functor /-
 /-- Converting a commutative monoid object in `Type` to a bundled commutative monoid.
 -/
 def functor : CommMon_ (Type u) ⥤ CommMonCat.{u}
@@ -119,7 +134,9 @@ def functor : CommMon_ (Type u) ⥤ CommMonCat.{u}
   obj A := ⟨A.pt⟩
   map A B f := MonTypeEquivalenceMon.functor.map f
 #align CommMon_Type_equivalence_CommMon.functor CommMonTypeEquivalenceCommMon.functor
+-/
 
+#print CommMonTypeEquivalenceCommMon.inverse /-
 /-- Converting a bundled commutative monoid to a commutative monoid object in `Type`.
 -/
 def inverse : CommMonCat.{u} ⥤ CommMon_ (Type u)
@@ -129,11 +146,13 @@ def inverse : CommMonCat.{u} ⥤ CommMon_ (Type u)
       mul_comm' := by ext ⟨x, y⟩; exact CommMonoid.mul_comm y x }
   map A B f := MonTypeEquivalenceMon.inverse.map f
 #align CommMon_Type_equivalence_CommMon.inverse CommMonTypeEquivalenceCommMon.inverse
+-/
 
 end commMonTypeEquivalenceCommMon
 
 open commMonTypeEquivalenceCommMon
 
+#print commMonTypeEquivalenceCommMon /-
 /-- The category of internal commutative monoid objects in `Type`
 is equivalent to the category of "native" bundled commutative monoids.
 -/
@@ -160,7 +179,9 @@ def commMonTypeEquivalenceCommMon : CommMon_ (Type u) ≌ CommMonCat.{u}
               map_mul' := fun x y => rfl } })
       (by tidy)
 #align CommMon_Type_equivalence_CommMon commMonTypeEquivalenceCommMon
+-/
 
+#print commMonTypeEquivalenceCommMonForget /-
 /-- The equivalences `Mon_ (Type u) ≌ Mon.{u}` and `CommMon_ (Type u) ≌ CommMon.{u}`
 are naturally compatible with the forgetful functors to `Mon` and `Mon_ (Type u)`.
 -/
@@ -169,8 +190,11 @@ def commMonTypeEquivalenceCommMonForget :
       CommMon_.forget₂Mon_ (Type u) ⋙ MonTypeEquivalenceMon.functor :=
   NatIso.ofComponents (fun A => Iso.refl _) (by tidy)
 #align CommMon_Type_equivalence_CommMon_forget commMonTypeEquivalenceCommMonForget
+-/
 
+#print commMonTypeInhabited /-
 instance commMonTypeInhabited : Inhabited (CommMon_ (Type u)) :=
   ⟨CommMonTypeEquivalenceCommMon.inverse.obj (CommMonCat.of PUnit)⟩
 #align CommMon_Type_inhabited commMonTypeInhabited
+-/
 

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

@@ -56,17 +56,9 @@ def inverse : MonCat.{u} ⥤ Mon_ (Type u)
     { pt := A
       one := fun _ => 1
       mul := fun p => p.1 * p.2
-      one_mul' := by
-        ext ⟨_, _⟩
-        dsimp
-        simp
-      mul_one' := by
-        ext ⟨_, _⟩
-        dsimp
-        simp
-      mul_assoc' := by
-        ext ⟨⟨x, y⟩, z⟩
-        simp [mul_assoc] }
+      one_mul' := by ext ⟨_, _⟩; dsimp; simp
+      mul_one' := by ext ⟨_, _⟩; dsimp; simp
+      mul_assoc' := by ext ⟨⟨x, y⟩, z⟩; simp [mul_assoc] }
   map A B f := { Hom := f }
 #align Mon_Type_equivalence_Mon.inverse MonTypeEquivalenceMon.inverse
 
@@ -134,9 +126,7 @@ def inverse : CommMonCat.{u} ⥤ CommMon_ (Type u)
     where
   obj A :=
     { MonTypeEquivalenceMon.inverse.obj ((forget₂ CommMonCat MonCat).obj A) with
-      mul_comm' := by
-        ext ⟨x, y⟩
-        exact CommMonoid.mul_comm y x }
+      mul_comm' := by ext ⟨x, y⟩; exact CommMonoid.mul_comm y x }
   map A B f := MonTypeEquivalenceMon.inverse.map f
 #align CommMon_Type_equivalence_CommMon.inverse CommMonTypeEquivalenceCommMon.inverse
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -4,13 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module category_theory.monoidal.internal.types
-! leanprover-community/mathlib commit 4d0b6301ef962e6bd74462998943ce38b7adb132
+! leanprover-community/mathlib commit 95a87616d63b3cb49d3fe678d416fbe9c4217bf4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Category.Mon.Basic
 import Mathbin.CategoryTheory.Monoidal.CommMon_
-import Mathbin.CategoryTheory.Monoidal.Types
+import Mathbin.CategoryTheory.Monoidal.Types.Symmetric
 
 /-!
 # `Mon_ (Type u) ≌ Mon.{u}`

mathlib commit https://github.com/leanprover-community/mathlib/commit/290a7ba01fbcab1b64757bdaa270d28f4dcede35

@@ -39,7 +39,8 @@ instance monMonoid (A : Mon_ (Type u)) : Monoid A.pt
 
 /-- Converting a monoid object in `Type` to a bundled monoid.
 -/
-def functor : Mon_ (Type u) ⥤ Mon.{u} where
+def functor : Mon_ (Type u) ⥤ MonCat.{u}
+    where
   obj A := ⟨A.pt⟩
   map A B f :=
     { toFun := f.Hom
@@ -49,7 +50,7 @@ def functor : Mon_ (Type u) ⥤ Mon.{u} where
 
 /-- Converting a bundled monoid to a monoid object in `Type`.
 -/
-def inverse : Mon.{u} ⥤ Mon_ (Type u)
+def inverse : MonCat.{u} ⥤ Mon_ (Type u)
     where
   obj A :=
     { pt := A
@@ -76,7 +77,7 @@ open monTypeEquivalenceMon
 /-- The category of internal monoid objects in `Type`
 is equivalent to the category of "native" bundled monoids.
 -/
-def monTypeEquivalenceMon : Mon_ (Type u) ≌ Mon.{u}
+def monTypeEquivalenceMon : Mon_ (Type u) ≌ MonCat.{u}
     where
   Functor := Functor
   inverse := inverse
@@ -104,12 +105,12 @@ def monTypeEquivalenceMon : Mon_ (Type u) ≌ Mon.{u}
 is naturally compatible with the forgetful functors to `Type u`.
 -/
 def monTypeEquivalenceMonForget :
-    MonTypeEquivalenceMon.functor ⋙ forget Mon ≅ Mon_.forget (Type u) :=
+    MonTypeEquivalenceMon.functor ⋙ forget MonCat ≅ Mon_.forget (Type u) :=
   NatIso.ofComponents (fun A => Iso.refl _) (by tidy)
 #align Mon_Type_equivalence_Mon_forget monTypeEquivalenceMonForget
 
 instance monTypeInhabited : Inhabited (Mon_ (Type u)) :=
-  ⟨MonTypeEquivalenceMon.inverse.obj (Mon.of PUnit)⟩
+  ⟨MonTypeEquivalenceMon.inverse.obj (MonCat.of PUnit)⟩
 #align Mon_Type_inhabited monTypeInhabited
 
 namespace commMonTypeEquivalenceCommMon
@@ -121,7 +122,7 @@ instance commMonCommMonoid (A : CommMon_ (Type u)) : CommMonoid A.pt :=
 
 /-- Converting a commutative monoid object in `Type` to a bundled commutative monoid.
 -/
-def functor : CommMon_ (Type u) ⥤ CommMon.{u}
+def functor : CommMon_ (Type u) ⥤ CommMonCat.{u}
     where
   obj A := ⟨A.pt⟩
   map A B f := MonTypeEquivalenceMon.functor.map f
@@ -129,10 +130,10 @@ def functor : CommMon_ (Type u) ⥤ CommMon.{u}
 
 /-- Converting a bundled commutative monoid to a commutative monoid object in `Type`.
 -/
-def inverse : CommMon.{u} ⥤ CommMon_ (Type u)
+def inverse : CommMonCat.{u} ⥤ CommMon_ (Type u)
     where
   obj A :=
-    { MonTypeEquivalenceMon.inverse.obj ((forget₂ CommMon Mon).obj A) with
+    { MonTypeEquivalenceMon.inverse.obj ((forget₂ CommMonCat MonCat).obj A) with
       mul_comm' := by
         ext ⟨x, y⟩
         exact CommMonoid.mul_comm y x }
@@ -146,7 +147,7 @@ open commMonTypeEquivalenceCommMon
 /-- The category of internal commutative monoid objects in `Type`
 is equivalent to the category of "native" bundled commutative monoids.
 -/
-def commMonTypeEquivalenceCommMon : CommMon_ (Type u) ≌ CommMon.{u}
+def commMonTypeEquivalenceCommMon : CommMon_ (Type u) ≌ CommMonCat.{u}
     where
   Functor := Functor
   inverse := inverse
@@ -174,12 +175,12 @@ def commMonTypeEquivalenceCommMon : CommMon_ (Type u) ≌ CommMon.{u}
 are naturally compatible with the forgetful functors to `Mon` and `Mon_ (Type u)`.
 -/
 def commMonTypeEquivalenceCommMonForget :
-    CommMonTypeEquivalenceCommMon.functor ⋙ forget₂ CommMon Mon ≅
+    CommMonTypeEquivalenceCommMon.functor ⋙ forget₂ CommMonCat MonCat ≅
       CommMon_.forget₂Mon_ (Type u) ⋙ MonTypeEquivalenceMon.functor :=
   NatIso.ofComponents (fun A => Iso.refl _) (by tidy)
 #align CommMon_Type_equivalence_CommMon_forget commMonTypeEquivalenceCommMonForget
 
 instance commMonTypeInhabited : Inhabited (CommMon_ (Type u)) :=
-  ⟨CommMonTypeEquivalenceCommMon.inverse.obj (CommMon.of PUnit)⟩
+  ⟨CommMonTypeEquivalenceCommMon.inverse.obj (CommMonCat.of PUnit)⟩
 #align CommMon_Type_inhabited commMonTypeInhabited
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -28,7 +28,7 @@ open CategoryTheory
 
 namespace monTypeEquivalenceMon
 
-instance monMonoid (A : Mon_ (Type u)) : Monoid A.x
+instance monMonoid (A : Mon_ (Type u)) : Monoid A.pt
     where
   one := A.one PUnit.unit
   mul x y := A.mul (x, y)
@@ -40,7 +40,7 @@ instance monMonoid (A : Mon_ (Type u)) : Monoid A.x
 /-- Converting a monoid object in `Type` to a bundled monoid.
 -/
 def functor : Mon_ (Type u) ⥤ Mon.{u} where
-  obj A := ⟨A.x⟩
+  obj A := ⟨A.pt⟩
   map A B f :=
     { toFun := f.Hom
       map_one' := congr_fun f.OneHom PUnit.unit
@@ -52,7 +52,7 @@ def functor : Mon_ (Type u) ⥤ Mon.{u} where
 def inverse : Mon.{u} ⥤ Mon_ (Type u)
     where
   obj A :=
-    { x := A
+    { pt := A
       one := fun _ => 1
       mul := fun p => p.1 * p.2
       one_mul' := by
@@ -114,7 +114,7 @@ instance monTypeInhabited : Inhabited (Mon_ (Type u)) :=
 
 namespace commMonTypeEquivalenceCommMon
 
-instance commMonCommMonoid (A : CommMon_ (Type u)) : CommMonoid A.x :=
+instance commMonCommMonoid (A : CommMon_ (Type u)) : CommMonoid A.pt :=
   { MonTypeEquivalenceMon.monMonoid A.toMon_ with
     mul_comm := fun x y => by convert congr_fun A.mul_comm (y, x) }
 #align CommMon_Type_equivalence_CommMon.CommMon_comm_monoid CommMonTypeEquivalenceCommMon.commMonCommMonoid
@@ -123,7 +123,7 @@ instance commMonCommMonoid (A : CommMon_ (Type u)) : CommMonoid A.x :=
 -/
 def functor : CommMon_ (Type u) ⥤ CommMon.{u}
     where
-  obj A := ⟨A.x⟩
+  obj A := ⟨A.pt⟩
   map A B f := MonTypeEquivalenceMon.functor.map f
 #align CommMon_Type_equivalence_CommMon.functor CommMonTypeEquivalenceCommMon.functor
 

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

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.monoidal.internal.types
-! leanprover-community/mathlib commit 95a87616d63b3cb49d3fe678d416fbe9c4217bf4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Category.MonCat.Basic
 import Mathlib.CategoryTheory.Monoidal.CommMon_
 import Mathlib.CategoryTheory.Monoidal.Types.Symmetric
 
+#align_import category_theory.monoidal.internal.types from "leanprover-community/mathlib"@"95a87616d63b3cb49d3fe678d416fbe9c4217bf4"
+
 /-!
 # `Mon_ (Type u) ≌ MonCat.{u}`
 

@@ -13,7 +13,7 @@ import Mathlib.CategoryTheory.Monoidal.CommMon_
 import Mathlib.CategoryTheory.Monoidal.Types.Symmetric
 
 /-!
-# `Mon_ (Type u) ≌ Mon.{u}`
+# `Mon_ (Type u) ≌ MonCat.{u}`
 
 The category of internal monoid objects in `Type`
 is equivalent to the category of "native" bundled monoids.
@@ -93,7 +93,7 @@ noncomputable def monTypeEquivalenceMon : Mon_ (Type u) ≌ MonCat.{u} where
 set_option linter.uppercaseLean3 false in
 #align Mon_Type_equivalence_Mon monTypeEquivalenceMon
 
-/-- The equivalence `Mon_ (Type u) ≌ Mon.{u}`
+/-- The equivalence `Mon_ (Type u) ≌ MonCat.{u}`
 is naturally compatible with the forgetful functors to `Type u`.
 -/
 noncomputable def monTypeEquivalenceMonForget :
@@ -166,8 +166,8 @@ noncomputable def commMonTypeEquivalenceCommMon : CommMon_ (Type u) ≌ CommMonC
 set_option linter.uppercaseLean3 false in
 #align CommMon_Type_equivalence_CommMon commMonTypeEquivalenceCommMon
 
-/-- The equivalences `Mon_ (Type u) ≌ Mon.{u}` and `CommMon_ (Type u) ≌ CommMon.{u}`
-are naturally compatible with the forgetful functors to `Mon` and `Mon_ (Type u)`.
+/-- The equivalences `Mon_ (Type u) ≌ MonCat.{u}` and `CommMon_ (Type u) ≌ CommMonCat.{u}`
+are naturally compatible with the forgetful functors to `MonCat` and `Mon_ (Type u)`.
 -/
 noncomputable def commMonTypeEquivalenceCommMonForget :
     CommMonTypeEquivalenceCommMon.functor ⋙ forget₂ CommMonCat MonCat ≅