Theorems · Definition · category theory

CategoryTheory.shrinkYonedaObjObjEquiv

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.LocallySmall.{w, v, u} C] →
      {X : C} → {Y : Cᵒᵖ} → (CategoryTheory.shrinkYoneda.{w, v, u}.obj X).obj Y ≃ (Opposite.unop Y ⟶ X)

The type (shrinkYoneda.obj X).obj Y is equivalent to Y.unop ⟶ X.

Defined in

Mathlib.CategoryTheory.ShrinkYoneda

Cited by

35 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmall