dc.creator | DIEGO ALEXANDER ACOSTA ALVAREZ | |
dc.date | 2016-08-27 | |
dc.date.accessioned | 2022-10-12T19:56:00Z | |
dc.date.available | 2022-10-12T19:56:00Z | |
dc.identifier | http://cimat.repositorioinstitucional.mx/jspui/handle/1008/733 | |
dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/4125161 | |
dc.description | Many interesting kind of geometric-algebraic stacks are defined as the quotient stack associated
to a groupoid in algebraic spaces. More precisely, if (U; R; s; t; c) is a groupoid in
algebraic spaces we have the quotient stack [U=R]. Some of them are quotients by the action
of a group space into an algebraic space. When we have 1-morphisms X 􀀀! Z and Y 􀀀! Z
of quotient stacks, some natural questions arise: if a fibre or a 2-fibre product exists, is this
also a quotient stack? If the answer is armative, what is the associated groupoid? What if
one of those 1-morphisms has an special property like to be an open immersion? In this work
we are going to give some results about these questions, trying to solve it in the most general
possible case.
While in categories over a fixed category C there are always a fibre product and a 2-fibre
product, when we are working with fibred categories we have found that a fibre product does
not always exist. However, we found a condition about the fibred product as a category over
C and a class of fibred categories and 1-morphisms for which fibre product can always be
constructed. We say that the fibre product has componentwise pullbacks if it satisfies that
condition. In particular, when we define a quotient stack as the stackification of the fibred
category associated to a functor induced by a groupoid in algebraic spaces, the fibred category
belongs to this class and we can take the fibre product | |
dc.format | application/pdf | |
dc.rights | info:eu-repo/semantics/openAccess | |
dc.rights | http://creativecommons.org/licenses/by-nc/4.0 | |
dc.subject | info:eu-repo/classification/MSC/FIBRED CATEGORIES | |
dc.subject | info:eu-repo/classification/cti/1 | |
dc.subject | info:eu-repo/classification/cti/12 | |
dc.subject | info:eu-repo/classification/cti/1299 | |
dc.subject | info:eu-repo/classification/cti/129999 | |
dc.title | SOME RESULTS IN QUOTIENT STACKS | |
dc.type | info:eu-repo/semantics/other | |
dc.type | info:mx-repo/semantics/doctoralDegreeWork | |
dc.type | info:eu-repo/semantics/acceptedVersion | |