Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app

∀ {B : Type u_1} [inst : CategoryTheory.Bicategory B] (F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat)
  {a b c d : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d) (X : ↑(F.obj a)),
  CategoryTheory.CategoryStruct.comp ((F.map h).toFunctor.map ((F.mapComp f g).inv.toNatTrans.app X))
      ((F.mapComp (CategoryTheory.CategoryStruct.comp f g) h).inv.toNatTrans.app X) =
    CategoryTheory.CategoryStruct.comp ((F.mapComp g h).inv.toNatTrans.app ((F.map f).toFunctor.obj X))
      (CategoryTheory.CategoryStruct.comp ((F.mapComp f (CategoryTheory.CategoryStruct.comp g h)).inv.toNatTrans.app X)
        ((F.map₂ (CategoryTheory.Bicategory.associator f g h).inv).toNatTrans.app X))

Defined in

Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor

Cited by

1 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory