Theorems · Theorem · category theory

CategoryTheory.shrinkYonedaEquiv_naturality

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

Defined in

Mathlib.CategoryTheory.ShrinkYoneda

Cited by

2 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmall