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dc.contributor.author
Dubuc, Eduardo Julio
dc.contributor.author
Szyld, Martín
dc.date.available
2017-07-07T19:49:52Z
dc.date.issued
2016
dc.identifier.citation
Dubuc, Eduardo Julio; Szyld, Martín; Tannaka theory over Sup-Lattices and Descent for Topoi; Mount Allison University; Theory And Applications Of Categories; 31; 31; 2016; 852-906
dc.identifier.issn
1201-561X
dc.identifier.uri
http://hdl.handle.net/11336/19886
dc.description.abstract
We consider locales B as algebras in the tensor category s` of sup-lattices. We show the equivalence between the Joyal-Tierney descent theorem for open localic surjections shB q −→ E in Galois theory and a Tannakian recognition theorem over s` for the s`-functor Rel(E) Rel(q ∗ ) −→ Rel(shB) ∼= (B-Mod)0 into the s`-category of discrete B-modules. Thus, a new Tannaka recognition theorem is obtained, essentially different from those known so far. This equivalence follows from two independent results. We develop an explicit construction of the localic groupoid G associated by Joyal-Tierney to q, and do an exhaustive comparison with the Deligne Tannakian construction of the Hopf algebroid L associated to Rel(q ∗ ), and show they are isomorphic, that is, L ∼= O(G). On the other hand, we show that the s`-category of relations of the classifying topos of any localic groupoid G, is equivalent to the s`-category of L-comodules with discrete subjacent B-module, where L = O(G). We are forced to work over an arbitrary base topos because, contrary to the neutral case which can be developed completely over Sets, here change of base techniques are unavoidable.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Mount Allison University
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Tannaka
dc.subject
Galois
dc.subject
Sup-Lattice
dc.subject
Locale
dc.subject
Topos
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Tannaka theory over Sup-Lattices and Descent for Topoi
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2017-06-26T14:09:18Z
dc.journal.volume
31
dc.journal.number
31
dc.journal.pagination
852-906
dc.journal.pais
Canadá
dc.description.fil
Fil: Dubuc, Eduardo Julio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.description.fil
Fil: Szyld, Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.journal.title
Theory And Applications Of Categories
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1510.01775
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://www.tac.mta.ca/tac/volumes/31/31/31-31abs.html
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