Theorems · Definition · category theory

CategoryTheory.Hom.monoid

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v, u_1} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] → {M X : C} → [CategoryTheory.MonObj M] → Monoid (X ⟶ M)

If M is a monoid object, then Hom(X, M) has a monoid structure.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mon

Cited by

52 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonObj