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3. Flatness of the Commutator Map Over $$\textrm{SL}_n$$

   https://doi.org/10.1093/imrn/rnz285  

   Larsen, Michael; Lu, Zhipeng (November 2019, International Mathematics Research Notices)

   Abstract Let $$K$$ be any field, and let $$n$$ be a positive integer. If we denote by $$\xi _{\textrm{SL}_n}\colon \textrm{SL}_n\times \textrm{SL}_n\to \textrm{SL}_n$$ the commutator morphism over $$K$$, then $$\xi _{\textrm{SL}_n}$$ is flat over the complement of the center of $$\textrm{SL}_n$$. 

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4. Super rewriting theory and nondegeneracy of odd categorified $$\mathfrak{sl}_{2}$$

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   Dupont, Benjamin; Ebert, Mark; Lauda, Aaron D (July 2024, Quantum Topology)

   We develop the rewriting theory for monoidal supercategories and2-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 for2-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\mathfrak{sl}(2)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 odd2-category conjectured by A. Lauda and I. Egilmez [Quantum Topol. 11 (2020), 227–294]. 

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