Theorems · Definition · category theory

CategoryTheory.AddMonObj.ofRepresentableBy

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v, u_1} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      (X : C) →
        (F : CategoryTheory.Functor Cᵒᵖ AddMonCat) →
          (F.comp (CategoryTheory.forget AddMonCat)).RepresentableBy X → CategoryTheory.AddMonObj X

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

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mon

Cited by

6 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory