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Dergiler / Journal of New Results in Science / 2023 / Cilt: 12 Sayı: 2

The universal property of commutative algebras' internal crossed modules

Elis SOYLU YILMAZ
Sayfa
77–85
Yayın Tarihi
2023-08-31
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Overall, in conclusion, we give a brief overview of the contributions and future research directions of the work presented, highlighting the significance of internal crossed modules in algebraic topology and category theory as well as making suggestions for possible areas of additional research and application.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this work, we identify subobjects and ideals in the category of internal crossed modules, which provide a deeper understanding of the structure of these objects.
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Temel Bulgular & Veri:Moreover, we provide several propositions through examples, which illustrate the properties and relationships between ideals and subobjects in the category of internal crossed modules.
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Sonuç & Katkı:Overall, in conclusion, we give a brief overview of the contributions and future research directions of the work presented, highlighting the significance of internal crossed modules in algebraic topology and category theory as well as making suggestions for possible areas of additional research and application.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Universal property · Internal crossed module · Ideal

Abstract

In this work, we identify subobjects and ideals in the category of internal crossed modules, which provide a deeper understanding of the structure of these objects. Moreover, we provide several propositions through examples, which illustrate the properties and relationships between ideals and subobjects in the category of internal crossed modules. The examples and propositions provided in this work can serve as a foundation for further research in this area and may lead to new insights and discoveries in the study of these complex algebraic structures. Overall, in conclusion, we give a brief overview of the contributions and future research directions of the work presented, highlighting the significance of internal crossed modules in algebraic topology and category theory as well as making suggestions for possible areas of additional research and application.

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Bu Makaleye Atıf Yap

YILMAZ, E. S. (2023). The universal property of commutative algebras' internal crossed modules. Journal of New Results in Science, Cilt: 12 Sayı: 2, 77–85. https://ajindex.com/articles/959575

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Kaynakça (17)

  1. J. H. C. Whitehead, Combinatorial homotopy II, Bulletin of American Mathematical Society 55 (5) (1949) 453-496.
  2. S. Lichtenbaum, M. Schlessinger, The cotangent complex of a morphism, Transactions of the American Mathematical Society 128 (1) (1967) 41-70.
  3. R. Brown, J. Huebschmann, Identities among relations. Low dimensional topology, London Mathematical Society Lecture Notes 46 (1982) 153-202.
  4. R. Brown, C. B. Spencer, G-groupoids, crossed modules and the fundamental groupoid of a topological group, In Indagationes Mathematicae (Proceedings) 79 (4) (1976) 296-302.
  5. T. Porter, Some categorical results in the theory of crossed modules in commutative algebras, Journal of Algebra 109 (2) (1987) 415-429.
  6. G. J. Ellis, Higher dimensional crossed modules of algebras, Journal of Pure and Applied Algebra 52 (3) (1988) 277-282.
  7. E. S. Yılmaz, K. Yılmaz, On crossed squares of commutative algebras, Mathematical Sciences and Applications E-Notes 8 (2) (2020) 32-41.
  8. Z. Arvasi, Crossed squares and 2-crossed modules of commutative algebras, Theory and Applications of Categories 3 (7) (1997) 160-181. K. Yılmaz, 2-Crossed modules over same base, Sakarya University Journal of Science 21 (6) (2017) 1210-1220.
  9. G. Ellis, Crossed squares and combinatorial homotopy, Mathematische Zeitschrift 214 (1) (1993) 93-110.
  10. K. Yılmaz, A fibration application for crossed squares, Cumhuriyet Science Journal 39 (1) (2018) 1-6.
  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. G. Janelidze, Internal crossed modules, Georgian Mathematical Journal 10 (1) (2003) 99-114.
  13. T. Porter, Extensions, crossed modules and internal categories in categories of groups with operations, Proceedings of the Edinburgh Mathematical Society 30 (3) (1987) 373-381.
  14. M. Forrester-Barker, Representations of crossed modules and cat$\pi$-groups, Doctoral Dissertation University of Wales (2003)
  15. Bangor. E. S. Yılmaz, U. E. Arslan, Internal cat-1 and XMod, Journal of New Theory (38) (2022) 79-87.
  16. U. E. Arslan, E. S. Yılmaz, On internal categories in higher dimensional groups, Journal of Universal Mathematics 5 (2) (2022) 129-138.
  17. N. M. Shammu, Algebraic and categorical structure of categories of crossed modules of algebras, Doctoral Dissertation University of North Carolina Wilmington (1992) Bangor. D. Conduché, Modules croisés généralisés de longueur 2, Journal of Pure and Applied Algebra 34 (2) (1984) 155-178. A. R. Grandjeán, M. J. Vale, 2-