Araştırma Makalesi
Yıl 2023,
Sayı: 42, 86 - 93, 31.03.2023
Öz
Kaynakça
- J. H. C. Whitehead, Combinatorial Homotopy II, Bulletin of American Mathematical Society 55 (5) (1949) 453–496.
- T. Porter, Homology of Commutative Algebras and an Invariant of Simis and Vasconcelos, Journal of Algebra 99 (2) (1986) 458–465.
- 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.
- 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.
- H. J. Baues, Combinatorial Homotopy and 4-dimensional Complexes, Walter de Gruyter, Berlin, 1991.
- Z. Arvasi and E. Ulualan, On Algebraic Models for Homotopy 3-types, Journal of Homotopy and Related Structures 1 (1) (2006) 1–27.
- Z. Arvasi, Crossed Squares and 2-Crossed Modules of Commutative Algebras, Theory and Applications of Categories 3 (1997) 160–181.
- G. J. Ellis, Higher Dimensional Crossed Modules of Algebras, Journal of Pure and Applied Algebra 52 (3) (1988) 277–282.
- E. S. Yılmaz, (Co)Limit Calculations in the Category of 2-crossed R-modules, Turkish Journal of Mathematics 46 (7) (2022) 2902–2915.
- A. Mutlu, T. Porter, Freeness Conditions for 2-crossed Modules 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.
- J. F. Martins, The Fundamental 2-crossed Complex of a Reduced CW-complex, Homology, Homotopy and Applications 13 (2) (2011) 129–157.
- K. H. Kamps, T. Porter, 2-groupoid Enrichments in Homotopy Theory and Algebra, K-theory 25 (4) (2002) 373–409.
- H. J. Baues, B. Bleile, Presentation of Homotopy Types under a Space (2010) 21 pages, https://arxiv.org/abs/1005.4810.
- E. S. Yılmaz, 4-Dimensional 2-Crossed Modules, Journal of New Theory (40) (2022) 46–53.
Yıl 2023,
Sayı: 42, 86 - 93, 31.03.2023
Öz
The study presents the direct product of two objects in the category of 4-dimensional 2-crossed modules. The structures of the domain, kernel, image, and codomain can be related using isomorphism theorems by defining the kernel and image of a morphism in a category. It then establishes the kernel and image of a morphism in the category of 4-dimensional 2-crossed modules to apply isomorphism theorems. These isomorphism theorems provide a powerful tool to understand the properties of this category. Moreover, isomorphism theorems in 4-dimensional 2-crossed modules allow us to establish connections between different algebraic structures and simplify complicated computations. Lastly, the present research inquires whether additional studies should be conducted.
Anahtar Kelimeler
Kaynakça
- J. H. C. Whitehead, Combinatorial Homotopy II, Bulletin of American Mathematical Society 55 (5) (1949) 453–496.
- T. Porter, Homology of Commutative Algebras and an Invariant of Simis and Vasconcelos, Journal of Algebra 99 (2) (1986) 458–465.
- 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.
- 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.
- H. J. Baues, Combinatorial Homotopy and 4-dimensional Complexes, Walter de Gruyter, Berlin, 1991.
- Z. Arvasi and E. Ulualan, On Algebraic Models for Homotopy 3-types, Journal of Homotopy and Related Structures 1 (1) (2006) 1–27.
- Z. Arvasi, Crossed Squares and 2-Crossed Modules of Commutative Algebras, Theory and Applications of Categories 3 (1997) 160–181.
- G. J. Ellis, Higher Dimensional Crossed Modules of Algebras, Journal of Pure and Applied Algebra 52 (3) (1988) 277–282.
- E. S. Yılmaz, (Co)Limit Calculations in the Category of 2-crossed R-modules, Turkish Journal of Mathematics 46 (7) (2022) 2902–2915.
- A. Mutlu, T. Porter, Freeness Conditions for 2-crossed Modules 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.
- J. F. Martins, The Fundamental 2-crossed Complex of a Reduced CW-complex, Homology, Homotopy and Applications 13 (2) (2011) 129–157.
- K. H. Kamps, T. Porter, 2-groupoid Enrichments in Homotopy Theory and Algebra, K-theory 25 (4) (2002) 373–409.
- H. J. Baues, B. Bleile, Presentation of Homotopy Types under a Space (2010) 21 pages, https://arxiv.org/abs/1005.4810.
- E. S. Yılmaz, 4-Dimensional 2-Crossed Modules, Journal of New Theory (40) (2022) 46–53.
Toplam 15 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Mart 2023 |
| Gönderilme Tarihi | 22 Kasım 2022 |
| Yayımlandığı Sayı | Yıl 2023 Sayı: 42 |
Kaynak Göster
- Makale Dosyaları