Theorems · Definition · category theory

CategoryTheory.Functor.mapMonNatTrans

{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 F' : CategoryTheory.Functor C D} →
              [inst_4 : F.LaxMonoidal] →
                [inst_5 : F'.LaxMonoidal] → (f : F ⟶ F') → [CategoryTheory.NatTrans.IsMonoidal f] → F.mapMon ⟶ F'.mapMon

Natural transformations between functors lift to monoid objects.

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.LaxMonoidalCategoryTheory.Functor.LaxMonoidalCategoryTheory.NatTrans.IsMonoidal