An embedding theorem for the category of crossed P-modules

EGE ARSLAN U., Onarli G.

GEORGIAN MATHEMATICAL JOURNAL, vol.22, no.3, pp.361-371, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 3
  • Publication Date: 2015
  • Doi Number: 10.1515/gmj-2015-0028
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.361-371
  • Eskisehir Osmangazi University Affiliated: Yes


In this paper, we show that the category of crossed modules over a fixed group is an exact category. We give a complete proof of the embedding theorem of XMod/P into a set-valued functor category. As a consequence of this theorem, we show that the subcategory of finitely generated free crossed P-modules is dense in the category of crossed P-modules and each crossed P-module is represented as a coend.