17/03/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building Pedro Resende, IST, CAMGSD
Facets of topos theory
Grothendieck toposes can be regarded in several ways, and in this talk I will give a bird's eye view of three such ways: (i) toposes as categories of sheaves (on sites, groupoids, quantales, etc.); (ii) as generalized universes of sets in which mathematics can be carried out; and (iii), last but not least, as generalized spaces in their own right, for instance orbit spaces of groupoids, with (noncommutative) quantales playing the role of "coordinate rings". I will begin with a crash course on locale theory, intended to provide the appropriate "commutative algebra".
