4-Dimensional 2-Crossed Modules

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.

A Note on 4-Dimensional 2-Crossed Modules

“…In this section, we will obtain the direct product of two given 4-dimensional 2-crossed modules. A 4-dimensional 2-crossed module [15] is a complex of algebras…”

“…Baues and Bleile developed the idea of 4-dimensional quadratic complexes [14] to examine the presentation of a space X as the mapping cone of a map ∂(X) beneath a space D for the algebraic description of pointed relative CW-complexes with cells in dimension 4. Based on the work of Baues and Bleile, the idea of 4-Dimensional 2-crossed modules was developed in [15] to examine any probable equivalence between homotopy 4-types. Moreover, subobjects and quotient objects in this category are defined in [15].…”

“…Based on the work of Baues and Bleile, the idea of 4-Dimensional 2-crossed modules was developed in [15] to examine any probable equivalence between homotopy 4-types. Moreover, subobjects and quotient objects in this category are defined in [15].…”