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Tagged with locally-presentable-categories gr.group-theory
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Which abelian groups are $\aleph_1$-filtered colimits of finitely-generated abelian groups?
Observation: Every $\aleph_1$-directed colimit $\varinjlim_i X_i$ of finite sets is finite.
Proof:
Because the $X_i$'s are finite, the Mittag-Leffler condition holds, so by passing to the diagram of ...
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