Groups up to congruence relation and from categorical groups to c-crossed modules


Datuashvili T., MUCUK O. , ŞAHAN T.

JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, vol.15, pp.625-640, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15
  • Publication Date: 2020
  • Doi Number: 10.1007/s40062-020-00270-4
  • Title of Journal : JOURNAL OF HOMOTOPY AND RELATED STRUCTURES
  • Page Numbers: pp.625-640

Abstract

We introduce a notion of c-group, which is a group up to congruence relation and consider the corresponding category. Extensions, actions and crossed modules (c-crossed modules) are defined in this category and the semi-direct product is constructed. We prove that each categorical group gives rise to a c-group and to a c-crossed module, which is a connected, special and strict c-crossed module in the sense defined by us. The results obtained here will be applied in the proof of an equivalence of the categories of categorical groups and connected, special and strict c-crossed modules.