On 2-algebras: crossed R-modules and categorical R-algebras

Abstract

In this work, we describe the category of categorical R-algebras and show that a categorical R-algebra is a category object in C = Alg(R). By using this property of categorical R-algebras, we can give an equivalency between the category of categorical R-algebras and the category of crossed R-modules and also the category of simplicial R-algebras.