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Some algebraic applications of graded categorical
group theory

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A.M. Cegarra and A.R. Garzon

The homotopy classification of graded categorical groups and their
homomorphisms is applied, in this paper, to obtain appropriate treatments
for diverse crossed product constructions with operators which appear in
several algebraic contexts. Precise classification theorems are therefore
stated for equivariant extensions by groups either of monoids, or groups,
or rings, or rings-groups or algebras as well as for graded Clifford
systems with operators, equivariant Azumaya algebras over Galois
extensions of commutative rings and for strongly graded bialgebras and
Hopf algebras with operators. These specialized classifications follow
from the theory of graded categorical groups after identifying, in each
case, adequate systems of factor sets with graded monoidal functors to
suitable graded categorical groups associated to the structure dealt with.

Keywords:
graded categorical group, graded monoidal functor, equivariant group
cohomology, crossed product, factor set, monoid extension, group
extension, ring-group
extension, Clifford system, Azumaya algebra, graded bialgebra, graded Hopf
algebra

2000 MSC:
18D10, 20J06, 20M10, 20M50, 16S35, 16W50, 16H05, 16W30

*Theory and Applications of Categories*
, Vol. 11, 2003,
No. 10, pp 215-251.

http://www.tac.mta.ca/tac/volumes/11/10/11-10.dvi

http://www.tac.mta.ca/tac/volumes/11/10/11-10.ps

http://www.tac.mta.ca/tac/volumes/11/10/11-10.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/11/10/11-10.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/11/10/11-10.ps

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