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, cilt.65, sa.3, ss.267-288, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 65 Sayı: 3
  • Basım Tarihi: 2022
  • Dergi Adı: Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.267-288
  • Anahtar Kelimeler: Cat1-algebroids, crossed modules of alge-broids, equivalence of categories, Peiffer ideal, precat1-algebroids, precrossed modules of algebroids
  • Uşak Üniversitesi Adresli: Evet

Özet

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.