Araştırma Makalesi
BibTex RIS Kaynak Göster

4-Dimensional 2-Crossed Modules

Yıl 2022, Sayı: 40, 46 - 53, 30.09.2022
https://doi.org/10.53570/jnt.1148482

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.

Kaynakça

  • 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.
Yıl 2022, Sayı: 40, 46 - 53, 30.09.2022
https://doi.org/10.53570/jnt.1148482

Öz

Kaynakça

  • 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.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Elis Soylu Yılmaz 0000-0002-0869-310X

Yayımlanma Tarihi 30 Eylül 2022
Gönderilme Tarihi 25 Temmuz 2022
Yayımlandığı Sayı Yıl 2022 Sayı: 40

Kaynak Göster

APA Soylu Yılmaz, E. (2022). 4-Dimensional 2-Crossed Modules. Journal of New Theory(40), 46-53. https://doi.org/10.53570/jnt.1148482
AMA Soylu Yılmaz E. 4-Dimensional 2-Crossed Modules. JNT. Eylül 2022;(40):46-53. doi:10.53570/jnt.1148482
Chicago Soylu Yılmaz, Elis. “4-Dimensional 2-Crossed Modules”. Journal of New Theory, sy. 40 (Eylül 2022): 46-53. https://doi.org/10.53570/jnt.1148482.
EndNote Soylu Yılmaz E (01 Eylül 2022) 4-Dimensional 2-Crossed Modules. Journal of New Theory 40 46–53.
IEEE E. Soylu Yılmaz, “4-Dimensional 2-Crossed Modules”, JNT, sy. 40, ss. 46–53, Eylül 2022, doi: 10.53570/jnt.1148482.
ISNAD Soylu Yılmaz, Elis. “4-Dimensional 2-Crossed Modules”. Journal of New Theory 40 (Eylül 2022), 46-53. https://doi.org/10.53570/jnt.1148482.
JAMA Soylu Yılmaz E. 4-Dimensional 2-Crossed Modules. JNT. 2022;:46–53.
MLA Soylu Yılmaz, Elis. “4-Dimensional 2-Crossed Modules”. Journal of New Theory, sy. 40, 2022, ss. 46-53, doi:10.53570/jnt.1148482.
Vancouver Soylu Yılmaz E. 4-Dimensional 2-Crossed Modules. JNT. 2022(40):46-53.


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