4-Dimensional 2-Crossed Modules

soylu yılmaz, elis

doi:10.53570/jnt.1148482

4-Dimensional 2-Crossed Modules

Elif SOYLU YILMAZ (Eskişehir Osmangazi Üniversitesi, Fen Fakültesi, Matematik ve Bilgisayar Bilimleri Bölümü, Eskişehir, Türkiye)

Journal of New Theory

2 1

Yıl: 2022 Cilt: Sayı: 40 Sayfa Aralığı: 46 - 53 Metin Dili: İngilizce DOI: 10.53570/jnt.1148482 İndeks Tarihi: 30-10-2022

4-Dimensional 2-Crossed Modules

Öz:

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.

Anahtar Kelime: Crossed Module subobject ideal category

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] D. Conduch ́e, Modules Crois ́es G ́en ́eralis ́es de Longueur 2, Journal of Pure and Applied Algebra 34 (2-3) (1984) 155–178.
[2] A. R. Grandje ́an, M. J. Vale, 2-Modulos Cruzados en la Cohomologia de Andr ́e-Quillen, Memorias de la Real Academia de Ciencias 22 (1986) 1–28.
[3] G. Ellis, Crossed Squares and Combinatorial Homotopy, Mathematische Zeitschrift 214 (1) (1993) 93–110.
[4] H. J. Baues, Combinatorial Homotopy and 4-Dimensional Complexes, Berlin, De Gruyter, 2011.
[5] 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.
[6] K. H. Kamps, T. Porter, 2-Groupoid Enrichments in Homotopy Theory and Algebra, K-theory 25 (4) (2002) 373–409.
[7] J. F. Martins, The Fundamental 2-Crossed Complex of a Reduced CW-Complex, Homology, Ho- motopy and Applications 13 (2) (2011) 129–157.
[8] H. J. Baues, B. Bleile, Presentation of Homotopy Types Under a Space, ArXiv Preprint, ArXiv:1005.4810, 2010.
[9] 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.
[10] R. Brown, I. I ̧cen, Homotopies and Automorphisms of Crossed Modules of Groupoids, Applied Categorical Structures 11 (2) (2003) 185–206.
[11] P. Carrasco, J. M. Moreno, Categorical G-Crossed Modules and 2-Fold Extensions, Journal of Pure and Applied Algebra 163 (3) (2001) 235–257.
[12] A. Mutlu, T. Porter, Freeness Conditions for 2-Crossed Codules and Complexes, Theory and Applications of Categories 4 (8) (1998) 174–194.
[13] A. Mutlu, Free 2-Crossed Complexes of Simplicial Algebras, Mathematical and Computational Applications 5 (1) (2000) 13–22.
[14] F. Wagemann, 2 Crossed Modules of Lie Algebras, Communications in Algebra 34 (5) (2006) 1699–1722.
[15] K. Yılmaz, E. Ulualan, Construction of Higher Groupoids via Matched Pairs Actions, Turkish Journal of Mathematics 43 (3) (2019) 1492-–1503.

APA	soylu yılmaz e (2022). 4-Dimensional 2-Crossed Modules. , 46 - 53. 10.53570/jnt.1148482
Chicago	soylu yılmaz elis 4-Dimensional 2-Crossed Modules. (2022): 46 - 53. 10.53570/jnt.1148482
MLA	soylu yılmaz elis 4-Dimensional 2-Crossed Modules. , 2022, ss.46 - 53. 10.53570/jnt.1148482
AMA	soylu yılmaz e 4-Dimensional 2-Crossed Modules. . 2022; 46 - 53. 10.53570/jnt.1148482
Vancouver	soylu yılmaz e 4-Dimensional 2-Crossed Modules. . 2022; 46 - 53. 10.53570/jnt.1148482
IEEE	soylu yılmaz e "4-Dimensional 2-Crossed Modules." , ss.46 - 53, 2022. 10.53570/jnt.1148482
ISNAD	soylu yılmaz, elis. "4-Dimensional 2-Crossed Modules". (2022), 46-53. https://doi.org/10.53570/jnt.1148482

APA	soylu yılmaz e (2022). 4-Dimensional 2-Crossed Modules. Journal of New Theory, (40), 46 - 53. 10.53570/jnt.1148482
Chicago	soylu yılmaz elis 4-Dimensional 2-Crossed Modules. Journal of New Theory , no.40 (2022): 46 - 53. 10.53570/jnt.1148482
MLA	soylu yılmaz elis 4-Dimensional 2-Crossed Modules. Journal of New Theory, vol., no.40, 2022, ss.46 - 53. 10.53570/jnt.1148482
AMA	soylu yılmaz e 4-Dimensional 2-Crossed Modules. Journal of New Theory. 2022; (40): 46 - 53. 10.53570/jnt.1148482
Vancouver	soylu yılmaz e 4-Dimensional 2-Crossed Modules. Journal of New Theory. 2022; (40): 46 - 53. 10.53570/jnt.1148482
IEEE	soylu yılmaz e "4-Dimensional 2-Crossed Modules." Journal of New Theory, , ss.46 - 53, 2022. 10.53570/jnt.1148482
ISNAD	soylu yılmaz, elis. "4-Dimensional 2-Crossed Modules". Journal of New Theory 40 (2022), 46-53. https://doi.org/10.53570/jnt.1148482