Theorems · Definition · category theory

CategoryTheory.Functor.addMonObjObj

{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.LaxMonoidal] → (X : C) → [CategoryTheory.AddMonObj X] → CategoryTheory.AddMonObj (F.obj X)

The image of an additive monoid object under a lax monoidal functor is an additive monoid object.

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

10 results in Mathlib

Foundations

Depth 10 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.LaxMonoidalCategoryTheory.AddMonObj