Pullback crossed modules in the category of racks


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EMİR K. , GÜLSÜN AKAY H.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.48, no.1, pp.140-149, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.15672/hjms.2017.532
  • Title of Journal : HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Page Numbers: pp.140-149

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.