Theorems · Theorem · category theory

CategoryTheory.Adjunction.mapCommMon_counit

∀ {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]
  {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C} (a : F ⊣ G) [inst_6 : F.Braided]
  [inst_7 : G.LaxBraided] [inst_8 : a.IsMonoidal],
  a.mapCommMon.counit =
    CategoryTheory.CategoryStruct.comp CategoryTheory.Functor.mapCommMonCompIso.inv
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.mapCommMonNatTrans a.counit)
        CategoryTheory.Functor.mapCommMonIdIso.hom)

Defined in

Mathlib.CategoryTheory.Monoidal.CommMon_

Cited by

0 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.Functor.BraidedCategoryTheory.Functor.LaxBraidedCategoryTheory.Adjunction.IsMonoidal