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