Theorems · Definition · category theory

CategoryTheory.Functor.mapComon

{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) →
              [F.OplaxMonoidal] → CategoryTheory.Functor (CategoryTheory.Comon C) (CategoryTheory.Comon D)

An oplax monoidal functor takes comonoid objects to comonoid objects. That is, an oplax monoidal functor F : C ⥤ D induces a functor Comon C ⥤ Comon D.

Defined in

Mathlib.CategoryTheory.Monoidal.Comon_

Cited by

4 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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