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Quasicomponents in topos theory: the hyperpure, complete spread factorization

Published online by Cambridge University Press:  12 February 2007

MARTA BUNGE  and
JONATHON FUNK
MARTA BUNGE
Affiliation:
Department of Mathematics, McGill University, Burnside Hall 805 Sherbrooke Street West Montreal, Quebec, CanadaH3A 2K6. e-mail: marta.bunge@mcgill.ca
JONATHON FUNK
Affiliation:
Dept. of Comp. Sci., Maths, and Physics, The University of the West Indies Cave Hill Campus, P.O. Box 64 Bridgetown, Barbados. e-mail: jfunk@uwichill.edu.bb
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Abstract

We establish the existence and uniqueness of a factorization for geometric morphisms that generalizes the pure, complete spread factorization for geometric morphisms with a locally connected domain. A complete spread with locally connected domain over a topos is a geometric counterpart of a Lawvere distribution on the topos, and the factorization itself is of the comprehensive type. The new factorization removes the topologically restrictive local connectedness requirement by working with quasicomponents in topos theory. In the special case when the codomain topos of the geometric morphism coincides with the base topos, the factorization gives the locale of quasicomponents of the domain topos, or its ‘0-dimensional’ reflection.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 1 , January 2007 , pp. 47 - 62
Copyright
Copyright © Cambridge Philosophical Society 2007

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