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Injective power objects and the axiom of choice. (English) Zbl 1208.03059
The author investigates the axiom of choice in a topos by interpreting the crucial term “non-empty” as being “injective”. He shows among other things that if the axiom of choice holds in the category of sets, then it holds in a wide variety of topoi, including all localic topoi, and that the topos-version has several of the classical consequences of the axiom of choice.

MSC:
03G30 Categorical logic, topoi
03E25 Axiom of choice and related propositions
18B25 Topoi
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References:
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