On universal gradings, versal gradings and Schurian generated categories

Autores
Cibils, Claude; Redondo, Maria Julia; Solotar, Andrea Leonor
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Categories over a field k can be graded by di erent groups in a connected way; we consider morphisms between these gradings in order to define the fundamental grading group. We prove that this group is isomorphic to the fundamental group à la Grothendieck as considered in previous papers. In case the k-category is Schurian generated we prove that a universal grading exists. Examples of non-Schurian generated categories with universal grading, versal grading or none of them are considered.
Fil: Cibils, Claude. Universite Montpellier Ii; Francia
Fil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Solotar, Andrea Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
grading
universal
versal
fundamental group
Schurian
Grothendieck
category
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/11970
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/11970
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On universal gradings, versal gradings and Schurian generated categoriesCibils, ClaudeRedondo, Maria JuliaSolotar, Andrea Leonorgradinguniversalversalfundamental groupSchurianGrothendieckcategoryhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Categories over a field k can be graded by di erent groups in a connected way; we consider morphisms between these gradings in order to define the fundamental grading group. We prove that this group is isomorphic to the fundamental group à la Grothendieck as considered in previous papers. In case the k-category is Schurian generated we prove that a universal grading exists. Examples of non-Schurian generated categories with universal grading, versal grading or none of them are considered.Fil: Cibils, Claude. Universite Montpellier Ii; FranciaFil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Solotar, Andrea Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaEuropean Mathematical Society2014-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/11970Cibils, Claude; Redondo, Maria Julia; Solotar, Andrea Leonor; On universal gradings, versal gradings and Schurian generated categories; European Mathematical Society; Journal of Noncommutative Geometry; 8; 4; 11-2014; 1101-11221661-6952enginfo:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=1661-6952&vol=8&iss=4&rank=7info:eu-repo/semantics/altIdentifier/url/http://dx.doi.org/10.4171/JNCG/180info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1210.4098info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:45:44Zoai:ri.conicet.gov.ar:11336/11970instacron: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:34982025-09-29 09:45:44.272CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On universal gradings, versal gradings and Schurian generated categories
title On universal gradings, versal gradings and Schurian generated categories
spellingShingle On universal gradings, versal gradings and Schurian generated categories
Cibils, Claude
grading
universal
versal
fundamental group
Schurian
Grothendieck
category
title_short On universal gradings, versal gradings and Schurian generated categories
title_full On universal gradings, versal gradings and Schurian generated categories
title_fullStr On universal gradings, versal gradings and Schurian generated categories
title_full_unstemmed On universal gradings, versal gradings and Schurian generated categories
title_sort On universal gradings, versal gradings and Schurian generated categories
dc.creator.none.fl_str_mv Cibils, Claude
Redondo, Maria Julia
Solotar, Andrea Leonor
author Cibils, Claude
author_facet Cibils, Claude
Redondo, Maria Julia
Solotar, Andrea Leonor
author_role author
author2 Redondo, Maria Julia
Solotar, Andrea Leonor
author2_role author
author
dc.subject.none.fl_str_mv grading
universal
versal
fundamental group
Schurian
Grothendieck
category
topic grading
universal
versal
fundamental group
Schurian
Grothendieck
category
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Categories over a field k can be graded by di erent groups in a connected way; we consider morphisms between these gradings in order to define the fundamental grading group. We prove that this group is isomorphic to the fundamental group à la Grothendieck as considered in previous papers. In case the k-category is Schurian generated we prove that a universal grading exists. Examples of non-Schurian generated categories with universal grading, versal grading or none of them are considered.
Fil: Cibils, Claude. Universite Montpellier Ii; Francia
Fil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Solotar, Andrea Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description Categories over a field k can be graded by di erent groups in a connected way; we consider morphisms between these gradings in order to define the fundamental grading group. We prove that this group is isomorphic to the fundamental group à la Grothendieck as considered in previous papers. In case the k-category is Schurian generated we prove that a universal grading exists. Examples of non-Schurian generated categories with universal grading, versal grading or none of them are considered.
publishDate 2014
dc.date.none.fl_str_mv 2014-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/11970
Cibils, Claude; Redondo, Maria Julia; Solotar, Andrea Leonor; On universal gradings, versal gradings and Schurian generated categories; European Mathematical Society; Journal of Noncommutative Geometry; 8; 4; 11-2014; 1101-1122
1661-6952
url http://hdl.handle.net/11336/11970
identifier_str_mv Cibils, Claude; Redondo, Maria Julia; Solotar, Andrea Leonor; On universal gradings, versal gradings and Schurian generated categories; European Mathematical Society; Journal of Noncommutative Geometry; 8; 4; 11-2014; 1101-1122
1661-6952
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=1661-6952&vol=8&iss=4&rank=7
info:eu-repo/semantics/altIdentifier/url/http://dx.doi.org/10.4171/JNCG/180
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1210.4098
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv European Mathematical Society
publisher.none.fl_str_mv European Mathematical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.069144

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