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dc.contributor.author
Descotte, María Emilia
dc.contributor.author
Dubuc, Eduardo Julio
dc.date.available
2017-12-04T19:48:45Z
dc.date.issued
2014-01
dc.identifier.citation
Descotte, María Emilia; Dubuc, Eduardo Julio; A theory of 2-Pro-objects; A.C. Ehresmann; Cahiers de Topologie Et Geometrie Differentielle Categoriques; LV; 1; 1-2014; 1-33
dc.identifier.issn
1245-530X
dc.identifier.uri
http://hdl.handle.net/11336/29615
dc.description.abstract
In [1], Grothendieck develops the theory of pro-objects over a category C . The fundamental property of the category Pro(C) is that there is an embedding C c −→ Pro(C), the category Pro(C) is closed under small cofiltered limits, and these limits are free in the sense that for any category E closed under small cofiltered limits, pre-composition with c determines an equivalence of categories Cat(Pro(C), E)+ 'Cat(C, E), (where the ” + ” indicates the full subcategory of the functors preserving cofiltered limits). In this paper we develop a 2-dimensional theory of pro-objects. Given a 2-category C , we define the 2-category 2-Pro(C) whose objects we call 2-pro-objects. We prove that 2-Pro(C) has all the expected basic properties adequately relativized to the 2-categorical setting, including the universal property corresponding to the one described above. We have at hand the results of Cat -enriched category theory, but our theory goes beyond the Cat -enriched case since we consider the non strict notion of pseudo-limit, which is usually that of practical interest.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
A.C. Ehresmann
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
2-Pro-Object
dc.subject
2-Filtered
dc.subject
Pseudo-Limit
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
A theory of 2-Pro-objects
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2017-06-23T14:13:02Z
dc.journal.volume
LV
dc.journal.number
1
dc.journal.pagination
1-33
dc.journal.pais
Francia
dc.description.fil
Fil: Descotte, María Emilia. 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: 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.journal.title
Cahiers de Topologie Et Geometrie Differentielle Categoriques
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/pdf/1406.5762.pdf
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://ehres.pagesperso-orange.fr/Cahiers/CTGDC%2055%202014/CahiersTopGDC%2055-1.pdf
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