On universal gradings, versal gradings and Schurian generated categories
Claude Cibils
Université de Montpellier 2, FranceMaría Julia Redondo
Universidad Nacional del Sur, Bahia Blanca, ArgentinaAndrea Solotar
Universidad de Buenos Aires, Argentina
![On universal gradings, versal gradings and Schurian generated categories cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jncg-volume-8-issue-4.png&w=3840&q=90)
Abstract
Categories over a field 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 -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.
Cite this article
Claude Cibils, María Julia Redondo, Andrea Solotar, On universal gradings, versal gradings and Schurian generated categories. J. Noncommut. Geom. 8 (2014), no. 4, pp. 1101–1122
DOI 10.4171/JNCG/180