Research Article
Year 2022,
Issue: 40, 46 - 53, 30.09.2022
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
References
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- R. Brown, I. I，cen, Homotopies and Automorphisms of Crossed Modules of Groupoids, Applied Categorical Structures 11 (2) (2003) 185–206.
- P. Carrasco, J. M. Moreno, Categorical G-Crossed Modules and 2-Fold Extensions, Journal of Pure and Applied Algebra 163 (3) (2001) 235–257.
- A. Mutlu, T. Porter, Freeness Conditions for 2-Crossed Codules and Complexes, Theory and Applications of Categories 4 (8) (1998) 174–194.
- A. Mutlu, Free 2-Crossed Complexes of Simplicial Algebras, Mathematical and Computational Applications 5 (1) (2000) 13–22.
- F. Wagemann, 2 Crossed Modules of Lie Algebras, Communications in Algebra 34 (5) (2006) 1699–1722.
- K. Yılmaz, E. Ulualan, Construction of Higher Groupoids via Matched Pairs Actions, Turkish Journal of Mathematics 43 (3) (2019) 1492–1503.
Year 2022,
Issue: 40, 46 - 53, 30.09.2022
Abstract
References
- D. Conduché, Modules Croisés Généralisés de Longueur 2, Journal of Pure and Applied Algebra 34 (2-3) (1984) 155–178.
- A. R. Grandjeán, M. J. Vale, 2-Modulos Cruzados en la Cohomologia de André-Quillen, Memorias de la Real Academia de Ciencias 22 (1986) 1–28.
- G. Ellis, Crossed Squares and Combinatorial Homotopy, Mathematische Zeitschrift 214 (1) (1993) 93–110.
- H. J. Baues, Combinatorial Homotopy and 4-Dimensional Complexes, Berlin, De Gruyter, 2011.
- R. Brown, N. D. Gilbert, Algebraic Models of 3-Types and Automorphism Structures for Crossed Modules, In Proceedings of the London Mathematical Society 59 (1) (1989) 51–73.
- K. H. Kamps, T. Porter, 2-Groupoid Enrichments in Homotopy Theory and Algebra, K-theory 25 (4) (2002) 373–409.
- J. F. Martins, The Fundamental 2-Crossed Complex of a Reduced CW-Complex, Homology, Homotopy and Applications 13 (2) (2011) 129–157.
- H. J. Baues, B. Bleile, Presentation of Homotopy Types Under a Space, ArXiv Preprint, ArXiv:1005.4810, 2010.
- U. E. Arslan, S. Kaplan, On Quasi 2-Crossed Modules for Lie Algebras and Functorial Relations, Ikonion Journal of Mathematics 4 (1) (2022) 17–26.
- R. Brown, I. I，cen, Homotopies and Automorphisms of Crossed Modules of Groupoids, Applied Categorical Structures 11 (2) (2003) 185–206.
- P. Carrasco, J. M. Moreno, Categorical G-Crossed Modules and 2-Fold Extensions, Journal of Pure and Applied Algebra 163 (3) (2001) 235–257.
- A. Mutlu, T. Porter, Freeness Conditions for 2-Crossed Codules and Complexes, Theory and Applications of Categories 4 (8) (1998) 174–194.
- A. Mutlu, Free 2-Crossed Complexes of Simplicial Algebras, Mathematical and Computational Applications 5 (1) (2000) 13–22.
- F. Wagemann, 2 Crossed Modules of Lie Algebras, Communications in Algebra 34 (5) (2006) 1699–1722.
- K. Yılmaz, E. Ulualan, Construction of Higher Groupoids via Matched Pairs Actions, Turkish Journal of Mathematics 43 (3) (2019) 1492–1503.
There are 15 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | September 30, 2022 |
| Submission Date | July 25, 2022 |
| Published in Issue | Year 2022 Issue: 40 |
Cite
Cited By
A Note on 4-Dimensional 2-Crossed Modules
Journal of New Theory
https://doi.org/10.53570/jnt.1208633
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