The category of generalized crossed modules

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YAVARI MAHDI; Salemkar Alireza

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Paper Information

Journal: CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS Year:2019 | Volume:10 | Issue:1 Page(s): 157-171

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Information Journal Paper

Title

The category of generalized crossed modules

Author(s)

YAVARI MAHDI | Salemkar Alireza | Issue Writer Certificate

Keywords

Group actionQ4

crossed moduleQ4

generalized crossed moduleQ4

categoryQ4

monomorphismQ4

epimorphismQ4

Abstract

In the definition of a crossed module (T, G, ), 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 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 that a generalized crossed module with which other actions (other than the conjugation) has the properties similar to a crossed module.

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APA: Copy

YAVARI, MAHDI, & Salemkar, Alireza. (2019). The category of generalized crossed modules. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, 10(1 ), 157-171. SID. https://sid.ir/paper/255413/en

Vancouver: Copy

YAVARI MAHDI, Salemkar Alireza. The category of generalized crossed modules. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS[Internet]. 2019;10(1 ):157-171. Available from: https://sid.ir/paper/255413/en

IEEE: Copy

MAHDI YAVARI, and Alireza Salemkar, “The category of generalized crossed modules,” CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, vol. 10, no. 1 , pp. 157–171, 2019, [Online]. Available: https://sid.ir/paper/255413/en

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