Graded extensions of categories

The problem of extending categories by groups, including theory of obstruct ions, is studied by means of factor systems and various homological invaria nts, generalized from Schreier-Eilenberg-Mac Lane group extension theory. E xplicit applications are then given to the classification of several algebr aic constructions long known as crossed products, appearing in many differe nt contexts such as monoids, Clifford systems or twisted group rings. (C) 2 000 Elsevier Science B.V. All rights reserved. MSG: 18D30; 18G50; 16S35.