Theorems · Definition · category theory

CategoryTheory.IsMonHom.monoidHom

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v, u_1} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      {M N : C} →
        [inst_2 : CategoryTheory.MonObj M] →
          [inst_3 : CategoryTheory.MonObj N] → (f : M ⟶ N) → [CategoryTheory.IsMonHom f] → (X : C) → (X ⟶ M) →* (X ⟶ N)

A monoid morphism f : M ⟶ N induces a monoid homomorphism M(X) →* N(X) for every X.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mon

Cited by

10 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonObjCategoryTheory.MonObjCategoryTheory.IsMonHom