Theorems · Theorem · category theory

CategoryTheory.Presheaf.freeYonedaHomEquiv_comp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {A : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} A]
  [inst_2 : CategoryTheory.Limits.HasCoproducts A] {X : C} {M : A} {F G : CategoryTheory.Functor Cᵒᵖ A}
  (α : CategoryTheory.Presheaf.freeYoneda X M ⟶ F) (f : F ⟶ G),
  CategoryTheory.Presheaf.freeYonedaHomEquiv (CategoryTheory.CategoryStruct.comp α f) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Presheaf.freeYonedaHomEquiv α) (f.app (Opposite.op X))

Defined in

Mathlib.CategoryTheory.Generator.Presheaf

Cited by

3 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasCoproducts