A theory of 2-Pro-objects
- Autores
- Descotte, María Emilia; Dubuc, Eduardo Julio
- Año de publicación
- 2014
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- 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.
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
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 - Materia
-
2-PRO-OBJECT
2-FILTERED
PSEUDO-LIMIT - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/29615
Ver los metadatos del registro completo
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A theory of 2-Pro-objectsDescotte, María EmiliaDubuc, Eduardo Julio2-PRO-OBJECT2-FILTEREDPSEUDO-LIMIThttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In [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.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; ArgentinaFil: Dubuc, Eduardo Julio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaA.C. Ehresmann2014-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/zipapplication/pdfhttp://hdl.handle.net/11336/29615Descotte, 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; 1-331245-530XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/pdf/1406.5762.pdfinfo:eu-repo/semantics/altIdentifier/url/http://ehres.pagesperso-orange.fr/Cahiers/CTGDC%2055%202014/CahiersTopGDC%2055-1.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:12:30Zoai:ri.conicet.gov.ar:11336/29615instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:12:31.151CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
A theory of 2-Pro-objects |
| title |
A theory of 2-Pro-objects |
| spellingShingle |
A theory of 2-Pro-objects Descotte, María Emilia 2-PRO-OBJECT 2-FILTERED PSEUDO-LIMIT |
| title_short |
A theory of 2-Pro-objects |
| title_full |
A theory of 2-Pro-objects |
| title_fullStr |
A theory of 2-Pro-objects |
| title_full_unstemmed |
A theory of 2-Pro-objects |
| title_sort |
A theory of 2-Pro-objects |
| dc.creator.none.fl_str_mv |
Descotte, María Emilia Dubuc, Eduardo Julio |
| author |
Descotte, María Emilia |
| author_facet |
Descotte, María Emilia Dubuc, Eduardo Julio |
| author_role |
author |
| author2 |
Dubuc, Eduardo Julio |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
2-PRO-OBJECT 2-FILTERED PSEUDO-LIMIT |
| topic |
2-PRO-OBJECT 2-FILTERED PSEUDO-LIMIT |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
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. 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 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 |
| description |
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. |
| publishDate |
2014 |
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2014-01 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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http://hdl.handle.net/11336/29615 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 1245-530X CONICET Digital CONICET |
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http://hdl.handle.net/11336/29615 |
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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 1245-530X CONICET Digital CONICET |
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eng |
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eng |
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