Theorems · Theorem · category theory

CategoryTheory.StrictPseudofunctor.comp_mapComp_hom

∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C] {D : Type u₃}
  [inst_2 : CategoryTheory.Bicategory D] (F : CategoryTheory.StrictPseudofunctor B C)
  (G : CategoryTheory.StrictPseudofunctor C D) {a b c : B} (f : a ⟶ b) (g : b ⟶ c),
  ((F.comp G).mapComp f g).hom =
    CategoryTheory.CategoryStruct.comp (G.map₂ (F.mapComp f g).hom) (G.mapComp (F.map f) (F.map g)).hom

Defined in

Mathlib.CategoryTheory.Bicategory.Functor.StrictPseudofunctor

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.BicategoryCategoryTheory.BicategoryCategoryTheory.Bicategory