Theorems · Definition · category theory

CategoryTheory.shrinkYonedaGrpObjObjEquiv

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.LocallySmall.{w, v, u} C] →
      [inst_2 : CategoryTheory.CartesianMonoidalCategory C] →
        {M : CategoryTheory.Grp C} →
          {Y : Cᵒᵖ} → ↑((CategoryTheory.shrinkYonedaGrp.{w, v, u}.obj M).obj Y) ≃* (Opposite.unop Y ⟶ M.X)

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

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.ShrinkYoneda

Cited by

3 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmallCategoryTheory.CartesianMonoidalCategory