Theorems · Theorem · category theory

CategoryTheory.shrinkYonedaObjObjEquiv_obj_map_assoc

∀ {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 : (CategoryTheory.shrinkYoneda.{w, v, u}.obj X).obj Y) {Z : C} (h : X ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.shrinkYonedaObjObjEquiv
        ((CategoryTheory.ConcreteCategory.hom ((CategoryTheory.shrinkYoneda.{w, v, u}.obj X).map g)) f))
      h =
    CategoryTheory.CategoryStruct.comp g.unop
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.shrinkYonedaObjObjEquiv f) h)

Defined in

Mathlib.CategoryTheory.ShrinkYoneda

Cited by

0 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmall