Super rewriting theory and nondegeneracy of odd categorified

  • Benjamin Dupont

    Université Claude Bernard Lyon 1, Villeurbanne, France
  • Mark Ebert

    University of Southern California, Los Angeles, USA; University of California, Los Angeles, USA
  • Aaron D. Lauda

    University of Southern California, Los Angeles, USA
Super rewriting theory and nondegeneracy of odd categorified $\mathfrak{sl}_{2}$ cover
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Abstract

We develop the rewriting theory for monoidal supercategories and -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 -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 from A. Ellis and A. Lauda [Quantum Topol. 7 (2016), 329–433] and J. Brundan and A. Ellis [Proc. Lond. Math. Soc. (3) 115 (2017), 925–973] As a corollary, this gives a classification of dg-structures on the odd -category conjectured by A. Lauda and I. Egilmez [Quantum Topol. 11 (2020), 227–294].

Cite this article

Benjamin Dupont, Mark Ebert, Aaron D. Lauda, Super rewriting theory and nondegeneracy of odd categorified . Quantum Topol. (2024), published online first

DOI 10.4171/QT/185