Theorems · Definition · category theory

CategoryTheory.Equivalence.mapMon

{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] →
            (e : C ≌ D) →
              [inst_4 : e.functor.Monoidal] →
                [inst_5 : e.inverse.Monoidal] → [e.IsMonoidal] → CategoryTheory.Mon C ≌ CategoryTheory.Mon D

An equivalence of categories lifts to an equivalence of their monoid objects.

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

4 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.MonoidalCategoryTheory.Functor.MonoidalCategoryTheory.Equivalence.IsMonoidal