4-Dimensional 2-Crossed Modules

Year 2022, Issue: 40, 46 - 53, 30.09.2022

Elis Soylu Yılmaz

https://doi.org/10.53570/jnt.1148482

Cited By: 1

Abstract

In this work, we defined a new category called 4-Dimensional 2-crossed modules. We identified the subobjects and ideals in this category. The notion of the subobject is a generalization of ideas like subsets from set theory, subspaces from topology, and subgroups from group theory. We then exemplified subobjects and ideals in the category of 4-Dimensional 2-crossed modules. A quotient object is the dual concept of a subobject. Concepts like quotient sets, spaces, groups, graphs, etc. are generalized with the notion of a quotient object. Using the ideal, we obtain the quotient of two subobjects and prove that the intersection of finite ideals is also an ideal in this category.

Keywords

Crossed Module, subobject, ideal, category

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