Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(4): 1077-1095

Printed July 31, 2015

https://doi.org/10.4134/BKMS.2015.52.4.1077

Copyright © The Korean Mathematical Society.

Equivariant crossed modules and cohomology of groups with operators

Pham Thi Cuc and Nguyen Tien Quang

Hongduc University, Hanoi National University of Education

Abstract

In this paper we study equivariant crossed modules in its link with strict graded categorical groups. The resulting Schreier theory for equivariant group extensions of the type of an equivariant crossed module generalizes both the theory of group extensions of the type of a crossed module and the one of equivariant group extensions.

Keywords: $\Gamma$-crossed module, strict graded categorical group, regular graded monoidal functor, equivariant extension, equivariant cohomology

MSC numbers: 18D10, 18D30, 20E22, 20J06

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