Pullback crossed modules in the category of racks
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.48, no.1, pp.140-149, 2019 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 48 Issue: 1
- Publication Date: 2019
- Doi Number: 10.15672/hjms.2017.532
- Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
- Page Numbers: pp.140-149
- Open Archive Collection: AVESIS Open Access Collection
- Eskisehir Osmangazi University Affiliated: Yes
Abstract
In this paper, we define the pullback crossed modules in the category of racks that are mainly based on a pullback diagram of rack morphisms with extra crossed module data on some of its arrows. Furthermore, we prove that the conjugation functor, which is defined between the category of crossed modules of groups and of racks, preserves the pullback crossed modules.