Theorems · Theorem · category theory

CategoryTheory.shrinkYoneda_map_app_shrinkYonedaObjObjEquiv_symm

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.LocallySmall.{w, v, u} C] {X X' : C}
  {Y : Cᵒᵖ} (f : Opposite.unop Y ⟶ X) (g : X ⟶ X'),
  (CategoryTheory.ConcreteCategory.hom ((CategoryTheory.shrinkYoneda.{w, v, u}.map g).app Y))
      (CategoryTheory.shrinkYonedaObjObjEquiv.symm f) =
    CategoryTheory.shrinkYonedaObjObjEquiv.symm (CategoryTheory.CategoryStruct.comp f g)

Defined in

Mathlib.CategoryTheory.ShrinkYoneda

Cited by

6 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmall