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arXiv · 1603.02592

Rewriting in higher dimensional linear categories and application to the affine oriented Brauer category

Clément Alleaume
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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.

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Clément Alleaume. 2016-03-01. Rewriting in higher dimensional linear categories and application to the affine oriented Brauer category. https://arxiv.org/abs/1603.02592

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