Theorems · Definition · category theory

CategoryTheory.AddGrpObj.ofRepresentableBy

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

If X represents a presheaf of additive monoids, then X is an additive monoid object.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Grp

Cited by

4 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory