Geodesic
A categorical account of the localic closed subgroup theorem
Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 3, pp. 541-553

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Given an axiomatic account of the category of locales the closed subgroup theorem is proved. The theorem is seen as a consequence of a categorical account of the Hofmann-Mislove theorem. The categorical account has an order dual providing a new result for locale theory: every compact subgroup is necessarily fitted.
Classification : 06D22, 06D50, 18B30, 18B40, 54B20, 54B30
Keywords: locale; power locale; Hofmann-Mislove theorem; closed subgroup; compact locale; fitted sublocale; categorical logic 
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Townsend, Christopher. A categorical account of the localic closed subgroup theorem. Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 3, pp. 541-553. http://geodesic.mathdoc.fr/item/CMUC_2007__48_3_a12/