On universal gradings, versal gradings and Schurian generated categories

Categories over a field k can be graded by different 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 t...

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Detalles Bibliográficos
Autores principales: Cibils, C., Redondo, M.J., Solotar, A.
Formato: JOUR
Materias:
Category
Fundamental group
Grading
Grothendieck
Schurian
Universal
Versal
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_16616952_v8_n4_p1101_Cibils
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_16616952_v8_n4_p1101_Cibils2023-10-03T16:28:41Z On universal gradings, versal gradings and Schurian generated categories Cibils, C. Redondo, M.J. Solotar, A. Category Fundamental group Grading Grothendieck Schurian Universal Versal Categories over a field k can be graded by different 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. © European Mathematical Society Fil:Redondo, M.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Solotar, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_16616952_v8_n4_p1101_Cibils
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Category
Fundamental group
Grading
Grothendieck
Schurian
Universal
Versal
spellingShingle Category
Fundamental group
Grading
Grothendieck
Schurian
Universal
Versal
Cibils, C.
Redondo, M.J.
Solotar, A.
On universal gradings, versal gradings and Schurian generated categories
topic_facet Category
Fundamental group
Grading
Grothendieck
Schurian
Universal
Versal
description Categories over a field k can be graded by different 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. © European Mathematical Society
format JOUR
author Cibils, C.
Redondo, M.J.
Solotar, A.
author_facet Cibils, C.
Redondo, M.J.
Solotar, A.
author_sort Cibils, C.
title On universal gradings, versal gradings and Schurian generated categories
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
url http://hdl.handle.net/20.500.12110/paper_16616952_v8_n4_p1101_Cibils
work_keys_str_mv AT cibilsc onuniversalgradingsversalgradingsandschuriangeneratedcategories
AT redondomj onuniversalgradingsversalgradingsandschuriangeneratedcategories
AT solotara onuniversalgradingsversalgradingsandschuriangeneratedcategories
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