Group theory MOC

Category of abelian groups

The category of abelian groups $𝖠 𝖻$ is a full subcategory of $𝖦 𝗋 𝗉$ containing abelian groups and homomorphisms between them. The category is equivalent to $ℤ 𝖬 𝗈 𝖽$ (Abelian groups as $ℤ$ -modules).

Properties

There is a Free-forgetful adjunction between the Abelianization $(-) a b : 𝖦 𝗋 𝗉 \to 𝖠 𝖻$ and the inclusion functor $I : 𝖠 𝖻 \to 𝖦 𝗋 𝗉$ .
Both the finitary product and coproduct is the Direct product of groups, hence it is an Additive category

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