Direct system of abelian groups
= Direct system of abelian groups
A direct system indexed by a <directed set> $A$ consists of <abelian groups> $G_a$ and homomorphisms $\phi_{ab}:G_a\to G_b$ for $a\leq b$, with $\phi_{aa}=1$ and $\phi_{bc}\phi_{ab}=\phi_{ac}$.