Publication: Pitts monads and a lax descent theorem
Dear colleagues, This is to announce that the following paper has been published and that it can be downloaded from the online journal Tbilisi Mathematical Journal. http://www.degruyter.com/view/j/tmj.2015.8.issue-1/tmj-2015-0001/tmj-2015-00... Marta Bunge, Pitts monads and a lax descent theorem,. Tbilisi Mathematical Journal, Volume 8, Issue 1, ISSN (Online) 1512-0139, DOI: 10.1515/tmj-2015-0001, February 2015 Abstract A theorem of A.M.Pitts (1986) states that essential surjections of toposes bounded over a base topos S are of effective lax descent. The symmetric monad M on the 2-category of toposes bounded over S is a KZ-monad (Bunge-Carboni 1995) and the M-maps are precisely the S-essential geometric morphisms (Bunge-Funk 2006). These last two results led me to conjecture and then prove the general lax descent theorem that is the subject matter of this paper. By a 'Pitts KZ-monad' on a 2-category K it is meant here a locally fully faithful equivariant KZ-monad M on K that is required to satisfy an analogue of Pitts' theorem on bicomma squares along essential geometric morphisms. The main result of this paper states that, for a Pitts KZ-monad M on a 2-category K ('of spaces'), every surjective M-map is of effective lax descent. There is a dual version of this theorem for a Pitts co-KZ-monad N. These theorems have (known and new) consequences regarding (lax) descent for morphisms of toposes and locales. Keywords: lax descent; Kock-Zoeberlein monads; symmetric monad; coherent toposes; powerlocales; Pitts' theorem. Cordially, Marta Bunge [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (1)
-
Marta Bunge