Theorems · Theorem · category theory

CategoryTheory.shrinkCoyonedaEquiv_naturality

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.LocallySmall.{w, v, u} C] {X Y : Cᵒᵖ}
  {P : CategoryTheory.Functor C (Type w)} (f : CategoryTheory.shrinkCoyoneda.{w, v, u}.obj X ⟶ P) (g : Y ⟶ X),
  (CategoryTheory.ConcreteCategory.hom (P.map g.unop)) (CategoryTheory.shrinkCoyonedaEquiv f) =
    CategoryTheory.shrinkCoyonedaEquiv
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.shrinkCoyoneda.{w, v, u}.map g) f)

Defined in

Mathlib.CategoryTheory.ShrinkYoneda

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmall