Theorems · Definition · category theory

CategoryTheory.Functor.mapCommMon

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      [inst_2 : CategoryTheory.BraidedCategory C] →
        {D : Type u₂} →
          [inst_3 : CategoryTheory.Category.{v₂, u₂} D] →
            [inst_4 : CategoryTheory.MonoidalCategory D] →
              [inst_5 : CategoryTheory.BraidedCategory D] →
                (F : CategoryTheory.Functor C D) →
                  [F.LaxBraided] → CategoryTheory.Functor (CategoryTheory.CommMon C) (CategoryTheory.CommMon D)

A lax braided functor takes commutative monoid objects to commutative monoid objects. That is, a lax braided functor F : C ⥤ D induces a functor CommMon C ⥤ CommMon D.

Defined in

Mathlib.CategoryTheory.Monoidal.CommMon_

Cited by

27 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.Functor.LaxBraided