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Monoidal supercategories. (English) Zbl 1396.17012
By now, there are several notions in the literature which are supposed to describe what should be called a super monoidal category. The goal of the paper under review is to clarify these notions and connections between them and in this way to develop a unified axiomatization for $$2$$-supercategories, that is $$2$$-categories enriched in vector superspaces, and related formal constructions. In particular, the paper discusses a superanalogue of the notion of Drinfeld center and considers $$2$$-supercategories with a fixed distinguished involution in its Drinfeld center. Gradings and Grothendieck groups in the supersetting are also discussed.

##### MSC:
 17B37 Quantum groups (quantized enveloping algebras) and related deformations 18D10 Monoidal, symmetric monoidal and braided categories (MSC2010) 18D05 Double categories, $$2$$-categories, bicategories and generalizations (MSC2010)
Zbl 1391.17011
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