Theorems · Definition · category theory

CategoryTheory.Equivalence.mapCommGrp

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      [inst_2 : CategoryTheory.BraidedCategory C] →
        {D : Type u₂} →
          [inst_3 : CategoryTheory.Category.{v₂, u₂} D] →
            [inst_4 : CategoryTheory.CartesianMonoidalCategory D] →
              [inst_5 : CategoryTheory.BraidedCategory D] →
                (e : C ≌ D) →
                  [e.functor.Braided] → [e.inverse.Braided] → CategoryTheory.CommGrp C ≌ CategoryTheory.CommGrp D

An equivalence of categories lifts to an equivalence of their commutative group objects.

Defined in

Mathlib.CategoryTheory.Monoidal.CommGrp_

Cited by

4 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.Functor.BraidedCategoryTheory.Functor.Braided