Theorems · Theorem · category theory

CategoryTheory.Functor.mapCommMonCompIso_hom_app_hom_hom

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] {D : Type u₂} [inst_3 : CategoryTheory.Category.{v₂, u₂} D]
  [inst_4 : CategoryTheory.MonoidalCategory D] [inst_5 : CategoryTheory.BraidedCategory D] {E : Type u₃}
  [inst_6 : CategoryTheory.Category.{v₃, u₃} E] [inst_7 : CategoryTheory.MonoidalCategory E]
  [inst_8 : CategoryTheory.BraidedCategory E] {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D E}
  [inst_9 : F.LaxBraided] [inst_10 : G.LaxBraided] (X : CategoryTheory.CommMon C),
  (CategoryTheory.Functor.mapCommMonCompIso.hom.app X).hom.hom = CategoryTheory.CategoryStruct.id (G.obj (F.obj X.X))

Defined in

Mathlib.CategoryTheory.Monoidal.CommMon_

Cited by

0 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.Functor.LaxBraidedCategoryTheory.Functor.LaxBraided