Journal of Noncommutative Geometry

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Volume 8, Issue 4, 2014, pp. 1101–1122
DOI: 10.4171/JNCG/180

Published online: 2015-02-02

On universal gradings, versal gradings and Schurian generated categories

Claude Cibils[1], María Julia Redondo[2] and Andrea Solotar[3]

(1) Université de Montpellier 2, France
(2) Universidad Nacional del Sur, Bahia Blanca, Argentina
(3) Universidad de Buenos Aires, Argentina

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.

Keywords: Grading, universal, versal, fundamental group, Schurian, Grothendieck, category

Cibils Claude, Redondo María Julia, Solotar Andrea: On universal gradings, versal gradings and Schurian generated categories. J. Noncommut. Geom. 8 (2014), 1101-1122. doi: 10.4171/JNCG/180