Theorems · Definition · category theory

CategoryTheory.Functor.mapAddMon

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      {D : Type u₂} →
        [inst_2 : CategoryTheory.Category.{v₂, u₂} D] →
          [inst_3 : CategoryTheory.MonoidalCategory D] →
            (F : CategoryTheory.Functor C D) →
              [F.LaxMonoidal] → CategoryTheory.Functor (CategoryTheory.AddMon C) (CategoryTheory.AddMon D)

A lax monoidal functor takes additive monoid objects to additive monoid objects. That is, a lax monoidal functor F : C ⥤ D induces a functor AddMon C ⥤ AddMon D.

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

28 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.LaxMonoidal