Theorems · Definition · category theory

CategoryTheory.Adjunction.rightAdjointLaxMonoidal

{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

The right adjoint of an oplax monoidal functor is lax monoidal.

Defined in

Mathlib.CategoryTheory.Monoidal.Functor

Cited by

2 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.OplaxMonoidal