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

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arxiv 1603.02592 v1 pith:FYH3SJBT submitted 2016-03-01 math.RT math.CT

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

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classification math.RT math.CT
keywords linearcategoriespolygraphsrewritingapplicationcategorydefinegive
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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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  1. Rewriting modulo isotopies in Khovanov-Lauda-Rouquier's categorification of quantum groups

    math.RT 2019-07 unverdicted novelty 7.0

    Rewriting modulo isotopies computes bases for 2-cells in the KLR 2-category that match Khovanov-Lauda conjectures, proving non-degeneracy and thus categorification of Lusztig's integral quantum group.