Theorems · Theorem · category theory

CategoryTheory.Functor.comp_mapCommMon_one

∀ {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] (A : CategoryTheory.CommMon C),
  CategoryTheory.MonObj.one =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.LaxMonoidal.ε (F.comp G))
      ((F.comp G).map CategoryTheory.MonObj.one)

Defined in

Mathlib.CategoryTheory.Monoidal.CommMon_

Cited by

0 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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