Theorems · Theorem · category theory

CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp_assoc

∀ {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 : M ⟶ F.obj (Opposite.op X)) (f : F ⟶ G) {Z : CategoryTheory.Functor Cᵒᵖ A} (h : G ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Presheaf.freeYonedaHomEquiv.symm α)
      (CategoryTheory.CategoryStruct.comp f h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Presheaf.freeYonedaHomEquiv.symm (CategoryTheory.CategoryStruct.comp α (f.app (Opposite.op X)))) h

Defined in

Mathlib.CategoryTheory.Generator.Presheaf

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasCoproducts