Theorems · Definition · category theory

CategoryTheory.Functor.mapMon

{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.Mon C) (CategoryTheory.Mon D)

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

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

38 results in Mathlib

Foundations

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

Assumes

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