Theorems · Inductive type · category theory

CategoryTheory.Adjunction.IsMonoidal

{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 : CategoryTheory.Functor C D} →
              {G : CategoryTheory.Functor D C} → (F ⊣ G) → [F.OplaxMonoidal] → [G.LaxMonoidal] → Prop

When adj : F ⊣ G is an adjunction, with F oplax monoidal and G lax-monoidal, this typeclass expresses compatibilities between the adjunction and the (op)lax monoidal structures.

Defined in

Mathlib.CategoryTheory.Monoidal.Functor

Cited by

20 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.OplaxMonoidalCategoryTheory.Functor.LaxMonoidal