category_theory.monoidal.skeleton
⟷
Mathlib.CategoryTheory.Monoidal.Skeleton
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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(last sync)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,7 +3,7 @@ Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
-import CategoryTheory.Monoidal.Braided
+import CategoryTheory.Monoidal.Braided.Basic
import CategoryTheory.Monoidal.Transport
import CategoryTheory.Skeletal
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,9 +3,9 @@ Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
-import Mathbin.CategoryTheory.Monoidal.Braided
-import Mathbin.CategoryTheory.Monoidal.Transport
-import Mathbin.CategoryTheory.Skeletal
+import CategoryTheory.Monoidal.Braided
+import CategoryTheory.Monoidal.Transport
+import CategoryTheory.Skeletal
#align_import category_theory.monoidal.skeleton from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.monoidal.skeleton
-! 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.Monoidal.Transport
import Mathbin.CategoryTheory.Skeletal
+#align_import category_theory.monoidal.skeleton from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
+
/-!
# The monoid on the skeleton of a monoidal category
mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
! This file was ported from Lean 3 source module category_theory.monoidal.skeleton
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! 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.Skeletal
/-!
# The monoid on the skeleton of a monoidal category
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
The skeleton of a monoidal category is a monoid.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -28,6 +28,7 @@ universe v u
variable {C : Type u} [Category.{v} C] [MonoidalCategory C]
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.monoidOfSkeletalMonoidal /-
/-- If `C` is monoidal and skeletal, it is a monoid.
See note [reducible non-instances]. -/
@[reducible]
@@ -39,11 +40,14 @@ def monoidOfSkeletalMonoidal (hC : Skeletal C) : Monoid C
mul_one X := hC ⟨ρ_ X⟩
mul_assoc X Y Z := hC ⟨α_ X Y Z⟩
#align category_theory.monoid_of_skeletal_monoidal CategoryTheory.monoidOfSkeletalMonoidal
+-/
+#print CategoryTheory.commMonoidOfSkeletalBraided /-
/-- If `C` is braided and skeletal, it is a commutative monoid. -/
def commMonoidOfSkeletalBraided [BraidedCategory C] (hC : Skeletal C) : CommMonoid C :=
{ monoidOfSkeletalMonoidal hC with mul_comm := fun X Y => hC ⟨β_ X Y⟩ }
#align category_theory.comm_monoid_of_skeletal_braided CategoryTheory.commMonoidOfSkeletalBraided
+-/
/-- The skeleton of a monoidal category has a monoidal structure itself, induced by the equivalence.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -3,7 +3,7 @@ Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
-import Mathlib.CategoryTheory.Monoidal.Braided
+import Mathlib.CategoryTheory.Monoidal.Braided.Basic
import Mathlib.CategoryTheory.Monoidal.Transport
import Mathlib.CategoryTheory.Skeletal
@@ -67,7 +67,7 @@ noncomputable instance instBraidedCategory [BraidedCategory C] : BraidedCategory
braidedCategoryOfFullyFaithful (Monoidal.fromTransported (skeletonEquivalence C).symm)
/--
-The skeleton of a braided monoidal category can be viewed as a commutative monoid, where the
+The skeleton of a braided monoidal category can be viewed as a commutative monoid, where the
multiplication is given by the tensor product, and satisfies the monoid axioms since it is a
skeleton.
-/
CommMonoid
instance (#7130)
This also names the instances so that the docstring can refer to them.
@@ -13,6 +13,12 @@ import Mathlib.CategoryTheory.Skeletal
# The monoid on the skeleton of a monoidal category
The skeleton of a monoidal category is a monoid.
+
+## Main results
+
+* `Skeleton.instMonoid`, for monoidal categories.
+* `Skeleton.instCommMonoid`, for braided monoidal categories.
+
-/
@@ -40,18 +46,34 @@ def commMonoidOfSkeletalBraided [BraidedCategory C] (hC : Skeletal C) : CommMono
{ monoidOfSkeletalMonoidal hC with mul_comm := fun X Y => hC ⟨β_ X Y⟩ }
#align category_theory.comm_monoid_of_skeletal_braided CategoryTheory.commMonoidOfSkeletalBraided
+namespace Skeleton
+
/-- The skeleton of a monoidal category has a monoidal structure itself, induced by the equivalence.
-/
-noncomputable instance : MonoidalCategory (Skeleton C) :=
+noncomputable instance instMonoidalCategory : MonoidalCategory (Skeleton C) :=
Monoidal.transport (skeletonEquivalence C).symm
/--
The skeleton of a monoidal category can be viewed as a monoid, where the multiplication is given by
the tensor product, and satisfies the monoid axioms since it is a skeleton.
-/
-noncomputable instance : Monoid (Skeleton C) :=
+noncomputable instance instMonoid : Monoid (Skeleton C) :=
monoidOfSkeletalMonoidal (skeletonIsSkeleton _).skel
--- TODO: Transfer the braided structure to the skeleton of C along the equivalence, and show that
--- the skeleton is a commutative monoid.
+/-- The skeleton of a braided monoidal category has a braided monoidal structure itself, induced by
+the equivalence. -/
+noncomputable instance instBraidedCategory [BraidedCategory C] : BraidedCategory (Skeleton C) :=
+ letI := Monoidal.instIsEquivalence_fromTransported (skeletonEquivalence C).symm
+ braidedCategoryOfFullyFaithful (Monoidal.fromTransported (skeletonEquivalence C).symm)
+
+/--
+The skeleton of a braided monoidal category can be viewed as a commutative monoid, where the
+multiplication is given by the tensor product, and satisfies the monoid axioms since it is a
+skeleton.
+-/
+noncomputable instance instCommMonoid [BraidedCategory C] : CommMonoid (Skeleton C) :=
+ commMonoidOfSkeletalBraided (skeletonIsSkeleton _).skel
+
+end Skeleton
+
end CategoryTheory
@@ -2,16 +2,13 @@
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.monoidal.skeleton
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! 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.Monoidal.Transport
import Mathlib.CategoryTheory.Skeletal
+#align_import category_theory.monoidal.skeleton from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
/-!
# The monoid on the skeleton of a monoidal category
All dependencies are ported!