Equivalence between (pre)cat1-R-algebroids and (pre)crossed modules of R-algebroids

AKÇA İ. İ., Avcio§gklu O.

Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, vol.65, no.3, pp.267-288, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 65 Issue: 3
  • Publication Date: 2022
  • Journal Name: Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.267-288
  • Keywords: Cat1-algebroids, crossed modules of alge-broids, equivalence of categories, Peiffer ideal, precat1-algebroids, precrossed modules of algebroids
  • Uşak University Affiliated: Yes

Abstract

In this study, we introduce (pre)cat1-R-algebroids, as a generalisation of cat1-algebras, and prove the equivalence between the categories of (pre)cat1-R-algebroids and (pre)crossed modules of R-algebroids. Moreover, we look over some immediate consequences of the equivalences and, as an application, for converting precat1-R-algebroids into cat1-R-algebroids we develop an equivalent method to the one used for converting precrossed modules into crossed modules of R-algebroids.