Presentations for tensor categories

2020/05/05 by James East, East, James · 2 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2005.01953

Abstract

We introduce new techniques for working with presentations for a large class of (strict) tensor categories. We then apply the general theory to obtain presentations for partition, Brauer and Temperley-Lieb categories, as well as several categories of (partial) braids, vines and mappings.

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• Affine diagram categories, algebras and monoids
• A presentation for the category of sl(3) webs and an extension of the quantum sl(3)-invariant to tangles

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