Theorems · Definition · category theory

CategoryTheory.Functor.mapCommGrpIdIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      [inst_2 : CategoryTheory.BraidedCategory C] →
        (CategoryTheory.Functor.id C).mapCommGrp ≅ CategoryTheory.Functor.id (CategoryTheory.CommGrp C)

The identity functor is also the identity on commutative group objects.

Defined in

Mathlib.CategoryTheory.Monoidal.CommGrp_

Cited by

6 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.BraidedCategory