CROSSED SEMIMODULES AND CAT(1)-MONOIDS


Temel S.

KOREAN JOURNAL OF MATHEMATICS, vol.27, no.2, pp.535-545, 2019 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.11568/kjm.2019.27.2.535
  • Journal Name: KOREAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.535-545
  • Keywords: Crossed module, crossed semimodule, cat(1)-group, cat(1)-monoid, INTERNAL CATEGORIES, TOPOLOGICAL-GROUPS, CO-HOMOLOGY, MODULES, GROUPOIDS, EXTENSIONS
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

The main idea of this paper is to introduce the notion of cat(1)-monoids and to prove that the category of crossed semimodules C = (A, B, partial derivative) where A is a group is equivalent to the category of cat(1)-monoids. This is a generalization of the well known equivalence between category of cat(1)-groups and that of crossed modules over groups.