The liftings of R-modules to covering groupoid

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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[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.