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

THE LIFTINGS OF R-MODULES TO COVERING GROUPOIDS

Nazmiye ALEMDAR
Osman MUCUK
Pages
813–822
Publication Date
2012-06-01
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:Group-groupoid · Covering groupoid · Topological R-module

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

ALEMDAR, N., MUCUK, O. (2012). THE LIFTINGS OF R-MODULES TO COVERING GROUPOIDS. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 6, 813–822. https://ajindex.com/articles/669624

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References (13)

  1. Bateson, A. Fundamental groups of topological R-modules, Trans. Amer. Math. Soc. 270 (2), –536, 1982.
  2. Brown, R. Topology and groupoids, (BookSurge 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 groups of non-connected topological groups revisited, Math. Proc. Camb. Phill. Soc. 115, 97–110, 1994.
  5. Brown, R. and Spencer, C. B. G-groupoids, crossed modules and the fundamental groupoid of a topological group, Proc. Konn. Ned. Akad. v. Wet. 79, 296–302, 1976.
  6. Chevalley, C. Theory of Lie groups, (Princeton University Press, United States of America, ). Higgins, P. J. Notes on categories and groupoids (Van Nostrand Reinhold Company, Durham, England, 1971).
  7. Mucuk, O., Kılı¸carslan, B., S¸ahan, T. and Alemdar, N. Group-groupoid and monodromy groupoid, Topology Appl. 158, 2034–2042, 2011.
  8. Mucuk, O. Covering groups of non-connected topological groups and the monodromy groupoid of a topological groupoid(PhD Thesis, University of Wales, 1993).
  9. Mucuk, O. Coverings and ring-groupoids, Geor. Math. J. 5, 475–482, 1998.
  10. Mucuk, O. and ¨Ozdemir, M, A monodromy principle for the universal covers of topological rings, Ind. J. Pure and Appl. Math. 31 (12), 1531–1535, 2000.
  11. Porter, T. Extensions, crossed modules and internal categories in categories of groups with operations, Proc. Edinb. Math. Soc. 30, 373–381, 1987.
  12. Rotman, J. J. An Introduction to Algebraic Topology (Graduate Texts in Mathematics 119, Springer-Verlag, New York, 1988).
  13. Taylor, R. L. Covering groups of non-connected topological groups, Proc. Amer. Math. Soc., 753–768, 1954.