Vitale, Enrico
[UCL]
A categorical group is a monoidal groupoid in which each object has a tensorial inverse. Two main examples are the Picard categorical group of a monoidal category and the Brauer categorical group of a braided monoidal category with stable coequalizers. After discussing the notions of kernel, cokemel and exact sequence for categorical groups, we show that, given a suitable monoidal functor between two symmetric monoidal categories with stable coequalizers, it is possible to build up a five-term Picard-Brauer exact sequence of categorical groups. The usual Units-Picard and Picard-Brauer exact sequences of abelian groups follow from this exact sequence of categorical groups. We also discuss the direct sum decomposition of the Brauer-Long group. (C) 2002 Elsevier Science B.V. All rights reserved.
Bibliographic reference |
Vitale, Enrico. A Picard-Brauer exact sequence of categorical groups. In: Journal of Pure and Applied Algebra, Vol. 175, no. 1-3, p. 383-408 (2002) |
Permanent URL |
http://hdl.handle.net/2078.1/41618 |