= Category of abelian groups
{title2=$\mathbf{Ab}$}
Objects are <abelian groups> and morphisms are <group homomorphisms>. Addition on hom-sets is pointwise, kernels are subgroup kernels, and cokernels are quotients by images. Thus this is an <abelian category>. Products are Cartesian products; coproducts are direct sums of finite-support families. The underlying-set <functor> creates directed colimits, giving a concrete description of their elements by eventual equality of representatives.
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