Theorems · Definition · category theory

CategoryTheory.Hom.commGroup

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      {G X : C} →
        [inst_2 : CategoryTheory.GrpObj G] →
          [inst_3 : CategoryTheory.BraidedCategory C] → [CategoryTheory.IsCommMonObj G] → CommGroup (X ⟶ G)

If G is a commutative group object, then Hom(X, G) has a commutative group structure.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Grp

Cited by

2 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.GrpObjCategoryTheory.BraidedCategoryCategoryTheory.IsCommMonObj