Theorems · Theorem · category theory

CategoryTheory.shrinkCoyoneda_obj_map_shrinkCoyonedaObjObjEquiv_symm

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

Defined in

Mathlib.CategoryTheory.ShrinkYoneda

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmall