Theorems · Theorem · category theory

CategoryTheory.Functor.functorHomEquiv_apply_app

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]
  (F G : CategoryTheory.Functor C D) (A : CategoryTheory.Functor C (Type (max u v v'))) (φ : A ⟶ F.functorHom G) (X : C)
  (a : A.obj X),
  ((F.functorHomEquiv G A) φ).app X a =
    ((CategoryTheory.ConcreteCategory.hom (φ.app X)) a).app X
      (CategoryTheory.CategoryStruct.id (Opposite.unop (Opposite.op X)))

Defined in

Mathlib.CategoryTheory.Functor.FunctorHom

Cited by

0 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category