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Dergiler / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 3

Construction of higher groupoids via matched pairs actions

Erdal ULUALAN
Koray YILMAZ
Sayfa
1492–1503
Yayın Tarihi
2022-11-05
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Given two 3-groupoids with a common edge, we construct a triple groupoid by using the matched pairs actions.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this work, we construct a relationship between matched pairs and triples of groupoids.
📊
Temel Bulgular & Veri:In this work, we construct a relationship between matched pairs and triples of groupoids.
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Sonuç & Katkı:Given two 3-groupoids with a common edge, we construct a triple groupoid by using the matched pairs actions.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this work, we construct a relationship between matched pairs and triples of groupoids. Given two 3-groupoids with a common edge, we construct a triple groupoid by using the matched pairs actions.

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Bu Makaleye Atıf Yap

ULUALAN, E., YILMAZ, K. (2022). Construction of higher groupoids via matched pairs actions. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 3, 1492–1503. https://ajindex.com/articles/607636

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Kaynakça (17)

  1. Brandt H. Ubereine verallgemeinerung des gruppenbegriffes. Mathematische Annalen 1926; 96: 360-366 (in German)
  2. Brown R. Groupoids and Van Kampen’s theorem. Proceedings of the London Mathematical Society 1967; 3: 385- 400
  3. Brown R. Fibration of groupoids. Journal of Algebra 1970; 15: 103-132
  4. Brown R. Groupoids as coefficients. Proceedings of the London Mathematical Society 1972; 3 (25): 413-426
  5. Brown R. Topology and Groupoids. Charleston, SC, USA: BookSurge Publishing, 2006
  6. Brown R. Double groupoids, matched pairs and then matched triples. https://arxiv.org/abs/1104.1644, 2011
  7. Brown R, Janelidze G. Galois theory and a new homotopy double groupoid of a map of spaces. Applied Categorical Structures 2004; 12: 63-80
  8. Brown R, Spencer C. Double groupoids and crossed modules. Cahiers de Topologie et Géométrie Différentielle Catégoriques 1976; 17: 343-364
  9. Ehresmann C. Catégories doubles et catégories structurées. Comptes Rendus Mathematique Academie des Sciences Paris 1963; 2569: 1198-1201 (in French)
  10. Gateva-Ivanova T, Majid S. Matched pairs approach to set theoretic solutions of the Yang–Baxter equation. Journal of Algebra 2008; 319: 1462–1529
  11. Higgins PJ. Notes on Categories and Groupoids. London, UK: Van Nostrand Reinhold, 1971
  12. Loday JL. Spaces with finitely many nontrivial homotopy groups. Journal of Pure and Applied Algebra 1982; 24: 179-202
  13. Majard D. N-tuple groupoids and optimally coupled factorizations. Theory and Application of Categories 2013; 28: 304-331
  14. Majid S. Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations. Pacific Journal of Mathematics 1990; 140: 311-332
  15. Majid S. Foundations of Quantum Group Theory. Cambridge, UK: Cambridge University Press, 1995
  16. Singer WM. Extension theory for connected Hopf algebras. Journal of Algebra 1972; 21: 1-16
  17. Takeuchi M. Matched pairs of groups and bismash products of Hopf algebras. Communications in Algebra 1981; 9: 841-882.