On rank one 2-representations of web categories

TL;DR

This paper classifies rank one 2-representations of specific web categories related to SL2, GL2, and SO3, using methods inspired by quantum group classifications, with adaptable approaches for other web categories.

Contribution

It provides a new classification framework for rank one 2-representations of web categories, extending techniques from quantum group theory.

Findings

Classified rank one 2-representations of SL2, GL2, and SO3 web categories.

Reduced classification to bilinear and trilinear form analysis.

Framework adaptable to other web categories.

Abstract

We classify rank one 2-representations of SL2, GL2 and SO3 web categories. The classification is inspired by similar results about quantum groups, given by reducing the problem to the classification of bilinear and trilinear forms, and is formulated such that it can be adapted to other web categories.