Symmetric closed categories and involutive Brauer groups (Q2738465)

The authors adapt a construction by \textit{E. M. Vitale} [Cah. Topologie Géom. Différ. Catégoriques 37, No. 2, 91-122 (1996; Zbl 0856.18007)] of the Brauer group of a symmetric monoidal category to construct a Brauer group of Azamaya algebras with involution for any symmetric closed category \(\mathcal C\). The resulting Brauer group generalizes involutive Brauer groups of \textit{R. Parimala} and \textit{V. Srinivas} [Duke Math. J. 66, No. 2, 207-237 (1992; Zbl 0780.13002)] and \textit{M. V. Reyes Sanchez} and the first author [Commun. Algebra 23, No. 14, 5269-5295 (1995; Zbl 0864.16013)]. The authors also define an involutive Picard group and obtain for a cofinal product-preserving functor of symmetric closed categories a 5-term exact sequence connecting the involutive Picard and Brauer groups, generalizing a well-known sequence of \textit{H. Bass} [Algebraic K-Theory, W. A. Benjamin, New York (1968; Zbl 0174.30302)].NEWLINENEWLINEFor the entire collection see [Zbl 0963.00025].