Theorems · Theorem · category theory

CategoryTheory.shrinkCoyonedaObjObjEquiv_obj_map

∀ {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 : (CategoryTheory.shrinkCoyoneda.{w, v, u}.obj X).obj Y),
  CategoryTheory.shrinkCoyonedaObjObjEquiv
      ((CategoryTheory.ConcreteCategory.hom ((CategoryTheory.shrinkCoyoneda.{w, v, u}.obj X).map g)) f) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.shrinkCoyonedaObjObjEquiv 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