Theorems · Theorem · category theory

CategoryTheory.Adjunction.mapMon_unit

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] {D : Type u₂}
  [inst_2 : CategoryTheory.Category.{v₂, u₂} D] [inst_3 : CategoryTheory.MonoidalCategory D]
  {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C} (a : F ⊣ G) [inst_4 : F.Monoidal]
  [inst_5 : G.LaxMonoidal] [inst_6 : a.IsMonoidal],
  a.mapMon.unit =
    CategoryTheory.CategoryStruct.comp CategoryTheory.Functor.mapMonIdIso.inv
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.mapMonNatTrans a.unit)
        CategoryTheory.Functor.mapMonCompIso.hom)

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.MonoidalCategoryTheory.Functor.LaxMonoidalCategoryTheory.Adjunction.IsMonoidal