Turkish Journal of Mathematics, cilt.45, sa.3, ss.1319-1336, 2021 (SCI-Expanded)
In this work, we describe the category of categorical R-algebras and show that a categorical R-algebra is a category object in C =AlgR. 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.