Theorems · Definition · category theory

CategoryTheory.Functor.FullyFaithful.mapCommMon

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      [inst_2 : CategoryTheory.BraidedCategory C] →
        {D : Type u₂} →
          [inst_3 : CategoryTheory.Category.{v₂, u₂} D] →
            [inst_4 : CategoryTheory.MonoidalCategory D] →
              [inst_5 : CategoryTheory.BraidedCategory D] →
                {F : CategoryTheory.Functor C D} → [inst_6 : F.Braided] → F.FullyFaithful → F.mapCommMon.FullyFaithful

If F : C ⥤ D is a fully faithful monoidal functor, then CommMonCat(F) : CommMonCat C ⥤ CommMonCat D is fully faithful too.

Defined in

Mathlib.CategoryTheory.Monoidal.CommMon_

Cited by

1 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.Functor.Braided