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On universal gradings, versal gradings and Schurian generated categories (1210.4098v2)
Published 15 Oct 2012 in math.CT and math.RA
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.