Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.rightZigzag_map

∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C] {a b : B}
  {f : a ⟶ b} {g : b ⟶ a} (F : CategoryTheory.Pseudofunctor B C) (adj : CategoryTheory.Bicategory.Adjunction f g),
  CategoryTheory.Bicategory.rightZigzag
      (CategoryTheory.CategoryStruct.comp (F.mapId a).inv
        (CategoryTheory.CategoryStruct.comp (F.map₂ adj.unit) (F.mapComp f g).hom))
      (CategoryTheory.CategoryStruct.comp (F.mapComp g f).inv
        (CategoryTheory.CategoryStruct.comp (F.map₂ adj.counit) (F.mapId b).hom)) =
    CategoryTheory.bicategoricalComp (CategoryTheory.Bicategory.whiskerLeft (F.map g) (F.mapId a).inv)
      (CategoryTheory.CategoryStruct.comp (F.mapComp g (CategoryTheory.CategoryStruct.id a)).inv
        (CategoryTheory.CategoryStruct.comp (F.map₂ (CategoryTheory.Bicategory.rightZigzag adj.unit adj.counit))
          (CategoryTheory.bicategoricalComp (F.mapComp (CategoryTheory.CategoryStruct.id b) g).hom
            (CategoryTheory.Bicategory.whiskerRight (F.mapId b).hom (F.map g)))))

Defined in

Mathlib.CategoryTheory.Bicategory.Adjunction.Basic

Cited by

0 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory