Theorems · Definition · category theory

CategoryTheory.yonedaGrpObjIsoOfRepresentableBy

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      (X : C) →
        (F : CategoryTheory.Functor Cᵒᵖ GrpCat) →
          (α : (F.comp (CategoryTheory.forget GrpCat)).RepresentableBy X) → CategoryTheory.yonedaGrpObj X ≅ F

If X represents a presheaf of groups F, then Hom(-, X) is isomorphic to F as a presheaf of groups.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Grp

Cited by

3 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory