Theorems · Definition · category theory

CategoryTheory.Hom.group

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] → {G X : C} → [CategoryTheory.GrpObj G] → Group (X ⟶ G)

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

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Grp

Cited by

25 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.GrpObj