A categorical account of the localic closed subgroup theorem

Christopher Townsend

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 3, page 541-553
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Townsend, Christopher. "A categorical account of the localic closed subgroup theorem." Commentationes Mathematicae Universitatis Carolinae 48.3 (2007): 541-553. <http://eudml.org/doc/250198>.

@article{Townsend2007,
abstract = {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.},
author = {Townsend, Christopher},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {locale; power locale; Hofmann-Mislove theorem; closed subgroup; compact locale; fitted sublocale; categorical logic; category of locales; group; subspace; open object; closed subset},
language = {eng},
number = {3},
pages = {541-553},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A categorical account of the localic closed subgroup theorem},
url = {http://eudml.org/doc/250198},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Townsend, Christopher
TI - A categorical account of the localic closed subgroup theorem
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 3
SP - 541
EP - 553
AB - 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.
LA - eng
KW - locale; power locale; Hofmann-Mislove theorem; closed subgroup; compact locale; fitted sublocale; categorical logic; category of locales; group; subspace; open object; closed subset
UR - http://eudml.org/doc/250198
ER -

References

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  7. MacLane S., Categories for the Working Mathematician, Graduate Texts in Mathematics 5, Springer, New York-Berlin, 1971. Zbl0705.18001MR1712872
  8. Townsend C.F., Vickers S.J., A universal characterization of the double power locale, Theoret. Comput. Sci. 316 (2004), 297-321. (2004) MR2074935
  9. Townsend C.F., An axiomatic account of weak localic triquotient assignments, J. Pure Appl. Algebra, to appear. 
  10. Townsend C.F., A categorical account of the Hofmann-Mislove theorem, Math. Proc. Cambridge Philos. Soc. 139 (2005), 441-456. (2005) Zbl1104.06008MR2177170
  11. Vickers S.J., Topology via Logic, Cambridge Tracts in Theoretical Computer Science 5, Cambridge University Press, Cambridge, 1989. Zbl0922.54002MR1002193

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