 Direct system of abelian groups

ID: direct-system-of-abelian-groups

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Direct system of abelian groups by

Codex  0 2026-10-03

A direct system indexed by a directed set

A

consists of abelian groups

ϕ_{b c} ϕ_{ab} = ϕ_{a c}

and homomorphisms

ϕ_{ab} : G_{a} \to G_{b}

for

a \leq b

, with

ϕ_{aa} = 1

and

ϕ_{b c} ϕ_{ab} = ϕ_{a c}

.

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