Theorems · Theorem · category theory

CategoryTheory.LaxFunctor.mapComp_assoc_left_assoc

∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C]
  (F : CategoryTheory.LaxFunctor B C) {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d) {Z : F.obj a ⟶ F.obj d}
  (h_1 : F.map (CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp f g) h) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight (F.mapComp f g) (F.map h))
      (CategoryTheory.CategoryStruct.comp (F.mapComp (CategoryTheory.CategoryStruct.comp f g) h) h_1) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.associator (F.map f) (F.map g) (F.map h)).hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (F.map f) (F.mapComp g h))
        (CategoryTheory.CategoryStruct.comp (F.mapComp f (CategoryTheory.CategoryStruct.comp g h))
          (CategoryTheory.CategoryStruct.comp (F.map₂ (CategoryTheory.Bicategory.associator f g h).inv) h_1)))

Defined in

Mathlib.CategoryTheory.Bicategory.Functor.Lax

Cited by

0 results in Mathlib

Foundations

Depth 8 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory