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
Keywords
Group-groupoid Covering groupoid Topological R-module R-module groupoid 2000 AMS Classification: 13 J xx
References
- Bateson, A. Fundamental groups of topological R-modules, Trans. Amer. Math. Soc. 270 (2), –536, 1982.
- Brown, R. Topology and groupoids, (BookSurge LLC, North Carolina, 2006).
- Brown, R. and Danesh-Naruie, G. The fundamental groupoid as a topological groupoid, Proc. Edinburgh Math. Soc. 19 (2), 237–244, 1975.
- Brown, R. and Mucuk, O. Covering groups of non-connected topological groups revisited, Math. Proc. Camb. Phill. Soc. 115, 97–110, 1994.
- 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.
- 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).
- Mucuk, O., Kılı¸carslan, B., S¸ahan, T. and Alemdar, N. Group-groupoid and monodromy groupoid, Topology Appl. 158, 2034–2042, 2011.
- Mucuk, O. Covering groups of non-connected topological groups and the monodromy groupoid of a topological groupoid(PhD Thesis, University of Wales, 1993).
- Mucuk, O. Coverings and ring-groupoids, Geor. Math. J. 5, 475–482, 1998.
- 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.
- Porter, T. Extensions, crossed modules and internal categories in categories of groups with operations, Proc. Edinb. Math. Soc. 30, 373–381, 1987.
- Rotman, J. J. An Introduction to Algebraic Topology (Graduate Texts in Mathematics 119, Springer-Verlag, New York, 1988).
- Taylor, R. L. Covering groups of non-connected topological groups, Proc. Amer. Math. Soc. , 753–768, 1954.
Abstract
References
- Bateson, A. Fundamental groups of topological R-modules, Trans. Amer. Math. Soc. 270 (2), –536, 1982.
- Brown, R. Topology and groupoids, (BookSurge LLC, North Carolina, 2006).
- Brown, R. and Danesh-Naruie, G. The fundamental groupoid as a topological groupoid, Proc. Edinburgh Math. Soc. 19 (2), 237–244, 1975.
- Brown, R. and Mucuk, O. Covering groups of non-connected topological groups revisited, Math. Proc. Camb. Phill. Soc. 115, 97–110, 1994.
- 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.
- 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).
- Mucuk, O., Kılı¸carslan, B., S¸ahan, T. and Alemdar, N. Group-groupoid and monodromy groupoid, Topology Appl. 158, 2034–2042, 2011.
- Mucuk, O. Covering groups of non-connected topological groups and the monodromy groupoid of a topological groupoid(PhD Thesis, University of Wales, 1993).
- Mucuk, O. Coverings and ring-groupoids, Geor. Math. J. 5, 475–482, 1998.
- 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.
- Porter, T. Extensions, crossed modules and internal categories in categories of groups with operations, Proc. Edinb. Math. Soc. 30, 373–381, 1987.
- Rotman, J. J. An Introduction to Algebraic Topology (Graduate Texts in Mathematics 119, Springer-Verlag, New York, 1988).
- Taylor, R. L. Covering groups of non-connected topological groups, Proc. Amer. Math. Soc. , 753–768, 1954.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | June 1, 2012 |
| Published in Issue | Year 2012 Volume: 41 Issue: 6 |