Theorems · Definition · category theory

CategoryTheory.Functor.FullyFaithful.mapAddMon

{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} → [inst_4 : F.Monoidal] → F.FullyFaithful → F.mapAddMon.FullyFaithful

If F : C ⥤ D is a fully faithful monoidal functor, then F.mapAddMon : AddMon C ⥤ AddMon D is fully faithful too.

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

1 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.Monoidal