bilimit_topos

bilimit_topos

[Eduardo J. Dubuc]

Dear colleagues,

I just put a new paper on the ArXiv, The details of the paper appear below.

Best wishes, eduardo Dubuc


http://arxiv.org/abs/1107.1685

A construction of 2-cofiltered bilimits of topoi
Authors: Eduardo J. Dubuc, Sergio Yuhjtman
(Submitted on 8 Jul 2011)

      Abstract: We show the existence of bilimits of 2-cofiltered
diagrams of topoi, generalizing the construction of cofiltered bilimits
developed in "SGA 4 Springer LNM 270 (1972)". For any given such
diagram, we show that it can be represented by a 2-cofiltered diagram of
small sites with finite limits, and we construct a small site for the
inverse limit topos. This is done by taking the 2-filtered bicolimit of
the underlying categories and inverse image functors. We use the
construction of this bicolimit developed in "A construction of
2-filtered bicolimits of categories, Cah. Top. et Geo. Diff. Vol.
XLVII-2 (2006)", where it is proved that if the categories in the
diagram have finite limits and the transition functors are exact, then
the bicolimit category has finite limits and the pseudocone functors are
exact. An application of our result here is the fact that every Galois
topos has points "2-Filteredness and the point of every Galois topos,
Proc. CT2007, App. Cat. St., Vol. 18, 2, (2010)".

Comments: 	7 pages
Subjects: 	Category Theory (math.CT)
Cite as: 	arXiv:1107.1685v1 [math.CT]


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