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- W2278890941 abstract "Given a particular collection of categorical axioms, aimed at capturing properties of the category of locales, we show that if (mathcal {C}) is a category that satisfies the axioms then so too is the category ([ G, mathcal {C}]) of G-objects, for any internal group G. To achieve this we prove a general categorical result: if an object S is double exponentiable in a category with finite products then so is its associated trivial G-object (S, π2:G × S → S). The result holds even if S is not exponentiable. An example is given of a category (mathcal {C}) that satisfies the axioms, but for which there is no elementary topos (mathcal {E}) such that (mathcal {C}) is the category of locales over (mathcal {E}). It is shown, in outline, how the results can be extended from groups to groupoids." @default.
- W2278890941 created "2016-06-24" @default.
- W2278890941 creator A5079745077 @default.
- W2278890941 date "2016-02-23" @default.
- W2278890941 modified "2023-09-25" @default.
- W2278890941 title "Stability of Properties of Locales Under Groups" @default.
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- W2278890941 doi "https://doi.org/10.1007/s10485-016-9430-6" @default.
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