Central extensions of precrossed modules
The cohomology of crossed modules studied by \textit{P. Carrasco, A. M. Cegarra} and \textit{A. R. Grandjeán} [J. Pure Appl. Algebra 168, 147--176 (2002; Zbl 0996.18010)] allowed the classification of crossed module central extensions. In this paper this result is extended to the category of precrossed modules (that is, crossed modules where Peiffer's condition does not hold). The authors prove that the second cohomology group of precrossed modules classifies the precrossed module central extensions. Then, a description of these central extensions is given by using a universal coefficient theorem for the (co)homology of precrossed modules that is also established in the paper.
scientific article; zbMATH DE number 2128568