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arXiv · 1210.4098

On universal gradings, versal gradings and Schurian generated categories

Claude Cibils·Maria Julia Redondo·Andrea Solotar
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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.

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Claude Cibils, Maria Julia Redondo, Andrea Solotar. 2013-03-11. On universal gradings, versal gradings and Schurian generated categories. https://arxiv.org/abs/1210.4098

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