Geodesic
Quasi locally connected toposes
Theory and applications of categories, Tome 18 (2007), pp. 209-239.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We have shown that complete spreads (with a locally connected domain) over a bounded topos E (relative to S) are `comprehensive' in the sense that they are precisely the second factor of a factorization associated with an instance of the comprehension scheme involving S-valued distributions on E. Lawvere has asked whether the `Michael coverings' (or complete spreads with a definable dominance domain) are comprehensive in a similar fashion. We give here a positive answer to this question. In order to deal effectively with the comprehension scheme in this context, we introduce a notion of an `extensive topos doctrine,' where the extensive quantities (or distributions) have values in a suitable subcategory of what we call `locally discrete' locales. In the process we define what we mean by a quasi locally connected topos, a notion that we feel may be of interest in its own right.
Classification : 18B25, 57M12, 18C15, 06E15
Keywords: complete spreads, distributions, zero-dimensional locales, comprehensive factorization 
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     author = {Marta Bunge and Jonathon Funk},
     title = {Quasi locally connected toposes},
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     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2007_18_a7/}
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Marta Bunge; Jonathon Funk. Quasi locally connected toposes. Theory and applications of categories, Tome 18 (2007), pp. 209-239. http://geodesic.mathdoc.fr/item/TAC_2007_18_a7/