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On universal gradings, versal gradings and Schurian generated categories
- Source :
- Journal of Noncommutative Geometry, Journal of Noncommutative Geometry, European Mathematical Society, 2014, 8 (4), pp.1101-1122. ⟨10.4171/JNCG/180⟩, CONICET Digital (CONICET), Consejo Nacional de Investigaciones Científicas y Técnicas, instacron:CONICET, J. Noncommut.. Geom., J. Noncommut. Geom., 2014, 8 (4), pp.1101-1122. 〈10.4171/JNCG/180〉
- Publication Year :
- 2014
- Publisher :
- HAL CCSD, 2014.
-
Abstract
- 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 \`a 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.<br />Comment: Final version to appear in the Journal of Noncommutative Geometry, 21 pages
- Subjects :
- Pure mathematics
Fundamental group
Matemáticas
Existential quantification
01 natural sciences
fundamental group
Matemática Pura
purl.org/becyt/ford/1 [https]
Morphism
versal
16W50, 55Q05, 18D20
Mathematics::Category Theory
0103 physical sciences
Direct sum decomposition
FOS: Mathematics
Category Theory (math.CT)
[ MATH.MATH-CT ] Mathematics [math]/Category Theory [math.CT]
0101 mathematics
Mathematical Physics
Mathematics
[MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT]
Algebra and Number Theory
Mathematics::Commutative Algebra
Homotopy
010102 general mathematics
Mathematics::Rings and Algebras
[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA]
purl.org/becyt/ford/1.1 [https]
universal
Mathematics - Category Theory
grading
Mathematics - Rings and Algebras
Automorphism
[ MATH.MATH-RA ] Mathematics [math]/Rings and Algebras [math.RA]
Grothendieck
Schurian
Rings and Algebras (math.RA)
category
Homogeneous
010307 mathematical physics
Geometry and Topology
CIENCIAS NATURALES Y EXACTAS
Vector space
Subjects
Details
- Language :
- English
- ISSN :
- 16616952 and 16616960
- Database :
- OpenAIRE
- Journal :
- Journal of Noncommutative Geometry, Journal of Noncommutative Geometry, European Mathematical Society, 2014, 8 (4), pp.1101-1122. ⟨10.4171/JNCG/180⟩, CONICET Digital (CONICET), Consejo Nacional de Investigaciones Científicas y Técnicas, instacron:CONICET, J. Noncommut.. Geom., J. Noncommut. Geom., 2014, 8 (4), pp.1101-1122. 〈10.4171/JNCG/180〉
- Accession number :
- edsair.doi.dedup.....99f6ea237d4ebbcc5ddee3242f1f3775