Theorems · Theorem · category theory

CategoryTheory.Presheaf.freeYoneda_map

∀ {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) {X_1 Y : Cᵒᵖ} (f : X_1 ⟶ Y),
  (CategoryTheory.Presheaf.freeYoneda X M).map f =
    CategoryTheory.Limits.Sigma.map' ⇑(CategoryTheory.ConcreteCategory.hom ((CategoryTheory.yoneda.obj X).map f))
      fun x => CategoryTheory.CategoryStruct.id M

Defined in

Mathlib.CategoryTheory.Generator.Presheaf

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasCoproducts