Theorems · Theorem · category theory

CategoryTheory.shrinkCoyonedaEquiv_symm_map

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.LocallySmall.{w, v, u} C] {X Y : C}
  (f : X ⟶ Y) {P : CategoryTheory.Functor C (Type w)} (t : P.obj X),
  CategoryTheory.shrinkCoyonedaEquiv.symm ((CategoryTheory.ConcreteCategory.hom (P.map f)) t) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.shrinkCoyoneda.{w, v, u}.map f.op)
      (CategoryTheory.shrinkCoyonedaEquiv.symm t)

Defined in

Mathlib.CategoryTheory.ShrinkYoneda

Cited by

1 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmall