Super rewriting theory and nondegeneracy of odd categorified sl(2)

2021/01/30 by Benjamin Dupont, Dupont, Benjamin, Mark Ebert +3
Mathematics · #17A70 #17B37 #20G42 #68Q42 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2102.00276

openalex publication_date 2021/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop the rewriting theory for monoidal supercategories and 2-supercategories. This extends the theory of higher-dimensional rewriting established for (linear) 2-categories to the super setting, providing a suite of tools for constructing bases and normal forms for 2-supercategories given by generators and relations. We then employ this newly developed theory to prove the non-degeneracy conjecture for the odd categorification of quantum sl(2) from arXiv:1307.7816 and arXiv:1701.04133. As a corollary, this gives a classification of dg-structures on the odd 2-category conjectured in arXiv:1808.04924.

Citations

• Linear polygraphs applied to categorification
• Rewriting in higher dimensional linear categories and application to the affine oriented Brauer category

Related

• The Khovanov-Lauda 2-category and categorifications of a level two quantum sl(n) representation
• Odd Khovanov homology, higher representation theory and higher rewriting theory
• Module categories over representations of SL_q(2) and graphs
• On 2-Verma modules for quantum \mathfraksl₂
• Module categories over representations of SL_q(2) in the non-semisimple case