Obstruction Theory for Extensions of Categorical Groups |
| |
Authors: | P. Carrasco A. R. Garzón |
| |
Affiliation: | (1) Departamento de Álgebra, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain |
| |
Abstract: | For any categorical group H, we introduce the categorical group Out(H) and then the well-known group exact sequence 1Z(H)HAut(H)Out(H)1 is raised to a categorical group level by using a suitable notion of exactness. Breen's Schreier theory for extensions of categorical groups is codified in terms of homomorphism to Out(H) and then we develop a sort of Eilenberg–Mac Lane obstruction theory that solves the general problem of the classification of all categorical group extensions of a group G by a categorical group H, in terms of ordinary group cohomology. |
| |
Keywords: | categorical group extension cohomology abstract kernel obstruction |
本文献已被 SpringerLink 等数据库收录! |
|