Theorems · Definition · category theory

CategoryTheory.yonedaMonObj

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v, u_1} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      (M : C) → [CategoryTheory.MonObj M] → CategoryTheory.Functor Cᵒᵖ MonCat

If M is a monoid object, then Hom(-, M) is a presheaf of monoids.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mon

Cited by

12 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonObj