Rewriting in higher dimensional linear categories and application to the affine oriented Brauer category
Representation Theory
2016-03-09 v1 Category Theory
Abstract
In this paper, we introduce a rewriting theory of linear monoidal categories. Those categories are a particular case of what we will define as linear (n, p)-categories. We will also define linear (n, p)-polygraphs, a linear adapation of n-polygraphs, to present linear (n -- 1, p)-categories. We focus then on linear (3, 2)-polygraphs to give presentations of linear monoidal categories. We finally give an application of this theory in linear (3, 2)-polygraphs to prove a basis theorem on the category AOB with a new method using a rewriting property defined by van Ostroom: decreasingness.
Keywords
Cite
@article{arxiv.1603.02592,
title = {Rewriting in higher dimensional linear categories and application to the affine oriented Brauer category},
author = {Clément Alleaume},
journal= {arXiv preprint arXiv:1603.02592},
year = {2016}
}