Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 10 1 2019 01 01 The category of generalized crossed modules 157 171 69897 10.29252/cgasa.10.1.157 EN Mahdieh Yavari Department of Mathematics, Shahid Beheshti University, G.C., Tehran 19839, Iran Alireza Salemkar Department of Mathematics, Shahid Beheshti University, G.C., Tehran 19839, Iran Journal Article 2018 04 17 In 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. https://cgasa.sbu.ac.ir/article_69897_042894bfec4f1e44310e2fc5853f599c.pdf