Theorems · Definition · category theory

CategoryTheory.yonedaGrpObjRepresentableBy

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      (G : C) →
        [inst_2 : CategoryTheory.GrpObj G] →
          ((CategoryTheory.yonedaGrpObj G).comp (CategoryTheory.forget GrpCat)).RepresentableBy G

If G is a monoid object, then Hom(-, G) as a presheaf of monoids is represented by G.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Grp

Cited by

1 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.GrpObj