Theorems · Definition · category theory

CategoryTheory.Functor.mapCommMonNatTrans

{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 F' : CategoryTheory.Functor C D} →
                  [inst_6 : F.LaxBraided] →
                    [inst_7 : F'.LaxBraided] →
                      (f : F ⟶ F') → [CategoryTheory.NatTrans.IsMonoidal f] → F.mapCommMon ⟶ F'.mapCommMon

Natural transformations between functors lift to monoid objects.

Defined in

Mathlib.CategoryTheory.Monoidal.CommMon_

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.Functor.LaxBraidedCategoryTheory.Functor.LaxBraidedCategoryTheory.NatTrans.IsMonoidal