A Note on 4-Dimensional 2-Crossed Modules

Year 2023, Issue: 42, 86 - 93, 31.03.2023

Koray Yılmaz

https://doi.org/10.53570/jnt.1208633

Abstract

The study presents the direct product of two objects in the category of 4-dimensional 2-crossed modules. The structures of the domain, kernel, image, and codomain can be related using isomorphism theorems by defining the kernel and image of a morphism in a category. It then establishes the kernel and image of a morphism in the category of 4-dimensional 2-crossed modules to apply isomorphism theorems. These isomorphism theorems provide a powerful tool to understand the properties of this category. Moreover, isomorphism theorems in 4-dimensional 2-crossed modules allow us to establish connections between different algebraic structures and simplify complicated computations. Lastly, the present research inquires whether additional studies should be conducted.

Keywords

Crossed module, kernel, image, category

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