I call to your atention the following yet unpublished papers: 1. arXiv:0706.1771 [ps, pdf, other] Title: The fundamental progroupoid of a general topos Authors: Eduardo J. Dubuc Comments: 19 pages Subjects: Category Theory (math.CT); Algebraic Topology (math.AT) Here we introduce a new notion of covering projections in a topos E. They are a particular kind of locally constant objects. When the topos is locally connected, all locally constant objects are covering projections. Given a fix cover U = {U_i}, we show how to construct the set of connected components in the topos E_U of covering projections trivialized by U, even if the topos E is not locally connected. Our theory generalize to an arbritrary topos the whole theory of the fundamental progroupoid known for locally connected topos. The following two papers are in the area of categorical topology, or topological categories. arXiv:math/0612727 [ps, pdf, other] Title: Quasitopoi over a base category Authors: Eduardo J. Dubuc, Luis Español Comments: 23 pages Subjects: Category Theory (math.CT) 3. arXiv:math/0611701 [ps, pdf, other] Title: Topological functors as familiarly-fibrations Authors: Eduardo J. Dubuc, Luis Español Comments: 16 pages Subjects: Category Theory (math.CT)
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Eduardo Dubuc