Theorems · Theorem · category theory

CategoryTheory.shrinkYonedaEquiv_symm_app_shrinkYonedaObjObjEquiv_symm

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.LocallySmall.{w, v, u} C] {X : C}
  {P : CategoryTheory.Functor Cᵒᵖ (Type w)} (s : P.obj (Opposite.op X)) {Y : C} (f : Y ⟶ X),
  (CategoryTheory.ConcreteCategory.hom ((CategoryTheory.shrinkYonedaEquiv.symm s).app (Opposite.op Y)))
      (CategoryTheory.shrinkYonedaObjObjEquiv.symm f) =
    (CategoryTheory.ConcreteCategory.hom (P.map f.op)) s

Defined in

Mathlib.CategoryTheory.ShrinkYoneda

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmall