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arXiv · 2602.11120

Monoidal 2-categories from foam evaluation

Leon J. Goertz·Laura Marino·Paul Wedrich
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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.

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Leon J. Goertz, Laura Marino, Paul Wedrich. 2026-02-11. Monoidal 2-categories from foam evaluation. https://arxiv.org/abs/2602.11120

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