Construction of higher groupoids via matched pairs actions

Yilmaz, Koray; Ulualan, Erdal

doi:10.3906/mat-1809-84

Cited by 1 publication

(1 citation statement)

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“…For the algebraic description of pointed relative CW-complexes with cells in dimensions 4, Baues and Bleile introduced the concept of 4-dimensional quadratic complexes [8] to investigate the presentation of a space X as mapping cone of a map ∂(X) under a space D. The need for a proper understanding of the relevant algebraic and categorical structure of the 4-Dimensional 2-crossed modules are motivated by studies and examples [9][10][11][12][13][14][15] for higher categorical structures. In this work, we defined the notion of 4-Dimensional 2-crossed modules in order to look into any potential equivalence between homotopy 4-types, which was inspired by the work of Baues and Bleile.…”

Section: Introductionmentioning

confidence: 99%

4-Dimensional 2-Crossed Modules

YILMAZ

2022

Journal of New Theory

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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.

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