Theorems · Definition · category theory

CategoryTheory.Functor.mapCommMonCompIso

{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] →
                {E : Type u₃} →
                  [inst_6 : CategoryTheory.Category.{v₃, u₃} E] →
                    [inst_7 : CategoryTheory.MonoidalCategory E] →
                      [inst_8 : CategoryTheory.BraidedCategory E] →
                        {F : CategoryTheory.Functor C D} →
                          {G : CategoryTheory.Functor D E} →
                            [inst_9 : F.LaxBraided] →
                              [inst_10 : G.LaxBraided] → (F.comp G).mapCommMon ≅ F.mapCommMon.comp G.mapCommMon

The composition functor is also the composition on commutative monoid objects.

Defined in

Mathlib.CategoryTheory.Monoidal.CommMon_

Cited by

6 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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