Monoidal 2-categories from foam evaluation
Quantum Algebra
2026-02-12 v1 Category Theory
Geometric Topology
Abstract
In this paper we describe a general framework for constructing examples of locally linear semistrict monoidal 2-categories covering many examples appearing in link homology theory. The main input datum is a closed foam evaluation formula. As examples, we rigorously construct semistrict monoidal 2-categories based on gl(N)-foams, which underlie the general linear link homology theories, and further examples based on Bar-Natan's decorated cobordisms, related to Khovanov homology. These monoidal 2-categories are typically non-semisimple, have duals for all objects, adjoints for all 1-morphisms, and carry a canonical spatial duality structure expressing oriented 3-dimensional pivotality and sphericality.
Cite
@article{arxiv.2602.11120,
title = {Monoidal 2-categories from foam evaluation},
author = {Leon J. Goertz and Laura Marino and Paul Wedrich},
journal= {arXiv preprint arXiv:2602.11120},
year = {2026}
}
Comments
56 pages, comments welcome