We define a 2-category that categorifies the covering Kac–Moody algebra for introduced by Clark and Wang. This categorification forms the structure of a super-2-category as formulated by Kang, Kashiwara, and Oh. The super-2-category structure introduces a -grading giving its Grothendieck group the structure of a free module over the group algebra of . By specializing the -action to +1 or to −1, the construction specializes to an “odd” categorification of and to a supercategorification of , respectively.
Cite this article
Alexander P. Ellis, Aaron D. Lauda, An odd categorification of . Quantum Topol. 7 (2016), no. 2, pp. 329–433DOI 10.4171/QT/78