Morphisms between categorified spin networks

TL;DR

This paper develops a graphical calculus for morphism spaces between categorified spin networks, enabling detailed analysis of their module structures using planar compositions of categorified Jones-Wenzl projectors.

Contribution

It introduces a new graphical calculus for categorified spin networks and applies it to study their module structures over colored unknots.

Findings

Graphical calculus for morphism spaces established

Module structure of spin networks analyzed using the calculus

Enhanced understanding of categorified spin network interactions

Abstract

We introduce a graphical calculus for computing morphism spaces between the categorified spin networks of Cooper and Krushkal. The calculus, phrased in terms of planar compositions of categorified Jones-Wenzl projectors and their duals, is then used to study the module structure of spin networks over the colored unknots.