Group theory MOC

Category of abelian groups

The category of abelian groups 𝖠𝖻 is a full subcategory of Category of groups containing abelian groups and homomorphisms between them. The category is equivalent to [[Category of left modules|ℤ𝖬𝗈𝖽]] (Abelian groups as Z-modules).

Properties

• There is a Free-forgetful adjunction between the Abelianization ( −)ab :𝖦𝗋𝗉 →𝖠𝖻 and the inclusion functor I :𝖠𝖻 →𝖦𝗋𝗉.
• Both the finitary product and coproduct is the Direct product of groups, hence it is an Additive category

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