Injective power objects and the axiom of choice
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.
scientific article; zbMATH DE number 5807454