Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-25T13:09:32.268Z Has data issue: false hasContentIssue false
  • English
  • Français

A Godement theorem for locales

Published online by Cambridge University Press:  04 October 2011

Anders Kock
Anders Kock
Affiliation:
Aarhus Universitet, Aarhus, Denmark
Get access Rights & Permissions [Opens in a new window]

Extract

The classical Godement Theorem for manifolds, characterizing kernel pairs for submersions (cf. e.g. [15], LG IV §5), has been used by Pradines[12] as a crucial property for having a good theory of differentiable groupoids; in fact, he developed an axiomatic theory of categories in which Godement's and some other exactness properties hold, under the name of ‘Godement diptych’.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 3 , May 1989 , pp. 463 - 471
Copyright
Copyright © Cambridge Philosophical Society 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Alta'ai, A. A.. Ph.D. thesis, Université Paul Sabatier, Toulouse (to appear).Google Scholar
[2] Gabriel, P.. Constructions de Préschémas Quotient. Sem. Géom. Algebrique (SGA 3), Lecture Notes in Math. vol. 151 (Springer-Verlag, 1970).Google Scholar
[3] Isbell, J., Kriz, I., Pultr, A. and Rosicky, J.. Remarks on localic groups. In Proc. of Louvainla-Neuve Conference 1987. Lecture Notes in Math. vol. 1348 (Springer-Verlag, 1988).Google Scholar
[4] Johnstone, P. T.. Stone Spaces. Cambridge Studies in Advanced Math. no. 3 (Cambridge University Press, 1982).Google Scholar
[5] Johnstone, P. T.. A constructive ‘closed subgroup theorem’ for localic groups and groupoids, Cahiers Topologie Géom. Differentielle Catégoriques (to appear).Google Scholar
[6] Joyal, A. and Tierney, M.. An Extension of the Galois Theory of Grothendieck. Memoirs Amer. Math. Soc. no. 309 (American Mathematical Society, 1984).Google Scholar
[7] Kock, A.. A Godement theorem for locales. Aarhus Preprint Series 1987/1988 no. 15.Google Scholar
[8] Moerdijk, I.. Continuous fibrations and inverse limits of toposes. Compositio Math. 58 (1986), 45–72.Google Scholar
[9] Moerdijk, I.. The classifying topos of a continuous groupoid. I. Trans. Amer. Math. Soc. (to appear).Google Scholar
[10] Moerdijk, I.. The classifying topos of a continuous groupoid. II. (To appear).Google Scholar
[11] Pitts, A.. Applications of sup-lattice enriched category theory to sheaf theory. Proc. London Math. Soc. (3) 57 (1988), 433–480.CrossRefGoogle Scholar
[12] Pradines, J.. Building categories in which a Godement's theorem is available. Cahiers Topologie Géom. Differentielle Catégoriques 16 (1975), 301–306.Google Scholar
[13] Pradines, J.. Charactérisation universelle du groupe fondamental d'un éspace de feuilles. (Preprint, 1985.)Google Scholar
[14] Pradines, J.. Lecture at Louvain-la-Neuve Category Meeting, 1987.Google Scholar
[15] Serre, J. P.. Lie Algebras and Lie Groups (Benjamin, 1965).Google Scholar