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

Authors: ZEKERİYA ARVASİ, ELİF ILGAZ ÇAĞLAYAN

Abstract: In this work, we describe the category of categorical $R$-algebras and show that a categorical $R$-algebra is a category object in $\mathcal{C=}A\lg _{R}$. 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.

Keywords: Category object, monoid object, categorical $R $-algebra, crossed $% R$-module, simplicial $R $-algebra

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