Theorems · Definition · category theory

CategoryTheory.Adjunction.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} →
                  {G : CategoryTheory.Functor D C} →
                    (a : F ⊣ G) →
                      [inst_6 : F.Braided] → [inst_7 : G.LaxBraided] → [a.IsMonoidal] → F.mapCommMon ⊣ G.mapCommMon

An adjunction of braided functors lifts to an adjunction of their lifts to commutative monoid objects.

Defined in

Mathlib.CategoryTheory.Monoidal.CommMon_

Cited by

2 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.Functor.BraidedCategoryTheory.Functor.LaxBraidedCategoryTheory.Adjunction.IsMonoidal