On universal gradings, versal gradings and Schurian generated categories
arXiv:1210.4098
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 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.
Final version to appear in the Journal of Noncommutative Geometry, 21 pages