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Results tagged with axiom-of-choice
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An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually disjoint nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets. The axiom of choice is related to the first of Hilbert's problems.
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Splitting lemma under assumption of the axiom of choice
I assume you are working in some fixed abelian category $\mathcal{A}$.
It is not true in general that every short exact sequence in $\mathcal{A}$ will split. The problem is that although you can pick …
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