Journals / Hacettepe Journal of Mathematics and Statistics / 2012 / Cilt: 41 - Sayı: 6

The liftings of R-modules to covering groupoid

Pages
813–822
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also prove similar results for a R-module object in the category of groupoids

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we prove that the group structure of a group object in the category of groupoids lifts to a covering groupoid.
📊
Key Findings & Data:In this paper we prove that the group structure of a group object in the category of groupoids lifts to a covering groupoid.
💡
Conclusion & Impact:We also prove similar results for a R-module object in the category of groupoids
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper we prove that the group structure of a group object in the category of groupoids lifts to a covering groupoid. We also prove similar results for a R-module object in the category of groupoids

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Cite This Article

MUCUK, O., ALEMDAR, N. (2022). The liftings of R-modules to covering groupoid. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 6, 813–822. https://ajindex.com/articles/530484

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References (14)

  1. Bateson, A. Fundamental groups of topological R-modules. Trans. Amer. Math. Soc. 270(2), 525-536, 1982
  2. Brown, R. Topology and groupoids, (BookSurgc LLC, North Carolina, 2006)
  3. Brown. R. and Danesh-Naruie, G. The fundamental groupoid as a topological groupoid, Proc. Edinburgh Math. Soc. 19(2), 237-244, 1975
  4. Brown, R. and Mucuk, O. Covering givups of non-connected topological groups revisited. Math. Proc. Cainb. Phill. Soc. 115, 97-110, 1994
  5. Brown. R. and Spencer, C. B. G-groupoid$, crossed modules and the fundamental groupoid of a topological givup, Proc. Konn. Ned- Akad. v. Wet. 79, 296 302, 1976
  6. Chevalley, C. Theory of Lie groups, (Princeton University Press. United States of America, 1946)
  7. Higgius, P. J. Notes on categories and groupoids (Van Nostraııd Reinhold Company, Durham, England, 1971)
  8. Mucuk, O., Kıhçarslan, B. Şalmn, T. and Alemdar, N. Group-groupoid and monodromy groupoid, Topology Appl. 158. 2034-2042, 2011
  9. Mucuk, O. Covering gro-ups of non-connected topological groups and the monodromy groujtoıd of a topological groupoid (PhD Thesis. University of Wales. 1993)
  10. Mucuk, O. Coverings and ring-groupoids, Geor. Math. J. 5, 475-482, 1998
  11. Mucuk, O. and Özdemir, M,.4 monodromy principle for the universal cxtvers of topological rings, Ind. J. Pure and Appl. Math. 31(12), 1531-1535, 2000
  12. Porter, T. Extensions, crossed modules and internal cattgories in calcgorits of givups with operations, Proc. Edinb. Math. Soc. 30, 373-381, 1987
  13. Rotinan, J.J. An Introduction to Algebraic Topology (Graduate Texts in Mathematics 119, Springer-Verlag, New York, 1988)
  14. Taylor, R. L. Covering groups of non-c&vpnected topcjlogical groups. Proc. Ainer. Math. Soc. 5, 753-768, 1954.