Theorems · Definition · category theory

CategoryTheory.yonedaMonObjIsoOfRepresentableBy

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

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

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mon

Cited by

3 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory