Graded extensions of monoidal categories

Abstract

The long-known results of Schreier-Eilenberg-Mac Lane on group extensions are raised to a categorical level, for the classification and construction of the manifold of all graded monoidal categories, the type being given group Γ with 1-component a given monoidal category. Explicit application is made to the classification of strongly graded bialgebras over commutative rings. © 2001 Academic Press.