Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585310120190101The category of generalized crossed modules15717169897ENMahdieh YavariDepartment of Mathematics, Shahid Beheshti University, G.C., Tehran 19839, IranAlireza SalemkarDepartment of Mathematics, Shahid Beheshti University, G.C., Tehran 19839, IranJournal Article20180417In the definition of a crossed module $(T,G,rho)$, the actions of the group $T$ and $G$ on themselves are given by conjugation. In this paper, we consider these actions to be arbitrary and thus generalize the concept of ordinary crossed module. Therefore, we get the category ${bf GCM}$, of all generalized crossed modules and generalized crossed module morphisms between them, and investigate some of its categorical properties. In particular, we study the relations between epimorphisms and the surjective morphisms, and thus generalize the corresponding results of the category of (ordinary) crossed modules. By generalizing the conjugation action, we can find out what is the superiority of the conjugation to other actions. Also, we can find out a generalized crossed module with which other actions (other than the conjugation) has the properties same as a crossed module.http://cgasa.sbu.ac.ir/article_69897_042894bfec4f1e44310e2fc5853f599c.pdf