Central extensions and internal groupoids in Maltsev categories
The author continues his study of internal groupoids in a Barr-exact Mal'tsev category, begun in an earlier paper in the same journal [\textit{M. Gran}, J. Pure Appl. Algebra 143, No. 1-3, 221-229 (1999; Zbl 0937.18006)]. In the earlier paper, he showed that the category of internal groupoids in such a category is itself a Barr-exact Mal'tsev category; this allows one to study the concept of central extension, as defined by \textit{G.~Janelidze} and \textit{G. M.~Kelly}, in such categories, and that is the goal of the present paper. In particular, the author obtains explicit descriptions of central extensions of crossed modules and of crossed rings.
scientific article; zbMATH DE number 1563010