Ibrahim Ilker Akça, Osman Avcioglu: Equivalence between (pre)cat$^{1}$-$R$-algebroids and (pre)crossed modules of $R$-algebroids, 267-288

Abstract:

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.

Key Words: Cat$^{1}$-algebroids, precat$^{1}$-algebroids, crossed modules of algebroids, precrossed modules of algebroids, equivalence of categories, Peiffer ideal.

2010 Mathematics Subject Classification: Primary 18E05, 18G45; Secondary 18A22, 18A35, 18A40.