Theorems · Theorem · category theory

CategoryTheory.shrinkYoneda_obj_map_shrinkYonedaObjObjEquiv_symm

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

Defined in

Mathlib.CategoryTheory.ShrinkYoneda

Cited by

5 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmall