Research Article
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Year 2023, Issue: 42, 86 - 93, 31.03.2023
https://doi.org/10.53570/jnt.1208633

Abstract

References

  • 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.

A Note on 4-Dimensional 2-Crossed Modules

Year 2023, Issue: 42, 86 - 93, 31.03.2023
https://doi.org/10.53570/jnt.1208633

Abstract

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.

References

  • 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.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Koray Yılmaz 0000-0002-8641-0603

Publication Date March 31, 2023
Submission Date November 22, 2022
Published in Issue Year 2023 Issue: 42

Cite

APA Yılmaz, K. (2023). A Note on 4-Dimensional 2-Crossed Modules. Journal of New Theory(42), 86-93. https://doi.org/10.53570/jnt.1208633
AMA Yılmaz K. A Note on 4-Dimensional 2-Crossed Modules. JNT. March 2023;(42):86-93. doi:10.53570/jnt.1208633
Chicago Yılmaz, Koray. “A Note on 4-Dimensional 2-Crossed Modules”. Journal of New Theory, no. 42 (March 2023): 86-93. https://doi.org/10.53570/jnt.1208633.
EndNote Yılmaz K (March 1, 2023) A Note on 4-Dimensional 2-Crossed Modules. Journal of New Theory 42 86–93.
IEEE K. Yılmaz, “A Note on 4-Dimensional 2-Crossed Modules”, JNT, no. 42, pp. 86–93, March 2023, doi: 10.53570/jnt.1208633.
ISNAD Yılmaz, Koray. “A Note on 4-Dimensional 2-Crossed Modules”. Journal of New Theory 42 (March 2023), 86-93. https://doi.org/10.53570/jnt.1208633.
JAMA Yılmaz K. A Note on 4-Dimensional 2-Crossed Modules. JNT. 2023;:86–93.
MLA Yılmaz, Koray. “A Note on 4-Dimensional 2-Crossed Modules”. Journal of New Theory, no. 42, 2023, pp. 86-93, doi:10.53570/jnt.1208633.
Vancouver Yılmaz K. A Note on 4-Dimensional 2-Crossed Modules. JNT. 2023(42):86-93.


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