Equivalence between (pre)cat(1)-R-algebroids and (pre)crossed modules of R-algebroids

AKÇA İ. İ., Avcioglu 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: Cat(1)-algebroids, precat(1)-algebroids, crossed modules of alge-broids, precrossed modules of algebroids, equivalence of categories, Peiffer ideal, CROSSED-MODULES, SPACES
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

In this study, we introduce (pre)cat(1)-R-algebroids, as a generalisation of cat(1)- algebras, and prove the equivalence between the categories of (pre)cat(1)-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 precat(1)-R-algebroids into cat(1)-R-algebroids we develop an equivalent method to the one used for converting precrossed modules into crossed modules of R-algebroids.