TY - JOUR
ID - 69897
TI - The category of generalized crossed modules
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Yavari, Mahdieh
AU - Salemkar, Alireza
AD - Department of Mathematics, Shahid Beheshti University, G.C., Tehran 19839, Iran
Y1 - 2019
PY - 2019
VL - 10
IS - 1
SP - 157
EP - 171
KW - Group action
KW - crossed module
KW - generalized crossed module
KW - category
KW - monomorphism
KW - epimorphism
DO -
N2 - 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.
UR - http://cgasa.sbu.ac.ir/article_69897.html
L1 - http://cgasa.sbu.ac.ir/article_69897_042894bfec4f1e44310e2fc5853f599c.pdf
ER -