Category of Abelian Groups

The category of abelian groups is the Full Subcategory of the Category of Groups that consists of all of the Abelian Groups.

Properties

• The category of abelian groups is a Reflective Subcategory of the category of groups, with the reflector given by Abelianization of a Group.

• The category of abelian groups is a Symmetric Monoidal Category with respect to the Tensor Product of Abelian Groups and the additive group $(\mathbb{Z},0,+)$ on the Integers.