Acknowledgement
We would like to thank the referee for helpful comments and suggestions, which improved the presentation of the paper.
References
- S.A Ahmadi, Generalized topological groups and genetic recombination, J Dyn Syst Geom Theor. 11 (2013), 51-58. https://doi.org/10.1080/1726037X.2013.823805
- H. F. Akiz, N. Alemdar, O. Mucuk and T. Sahan, Coverings of internal groupoids and crossed modules in the category of groups with operations, Georgian Math. Journal. 20 (2) (2013), 223-238. https://doi.org/10.1515/gmj-2013-0021
- J.T.Akinmoyewa, A study of some properties of generalized groups, Octogon Mathematical Magazine. 17 (2009), 125-134. https://www.uni-miskolc.hu/~matsefi/Octogon/volumes/volume2/article2_8.pdf
- J.C. Baez, A.D. Lauda, Higher-dimensional algebra V: 2-groups, Theory Appl. Categ. 12 (2004), 423-491. https://doi.org/10.48550/arXiv.math/0307200
- R. Brown, Topology and groupoids, Booksurge PLC, (2006). https://groupoids.org.uk/pdffiles/topgrpds-e.pdf
- R. Brown, Higher dimensional group theory, Low Dimensional Topology, London Math. Soc. Lect. Notes, Cambridge Univ. Press, 48, (1982) 215-238. https://doi.org/10.1017/CBO9780511758935.012
- R. Brown, O. Mucuk, Covering groups of non-connected topological groups revisited, Math. Proc. Camb. Phill. Soc. 115 (1994), 97-110. https://doi.org/10.1017/S0305004100071942
- R. Brown, C.B. Spencer, G-groupoids, crossed modules and the fundamental groupoid of a topological group, Proc. Konn. Ned. Akad. v. Wet. 79 (1976), 296-302. https://doi.org/10.1016/1385-7258(76)90068-8
- R. Brown, C.B. Spencer, Double groupoids and crossed modules, Cah. Topol. Geom. Differ. Categ. 17 (1976), 343-362. http://www.numdam.org/item?id=CTGDC_1976__17_4_343_0
- R. Brown, P. J. Higgins, R. Sivera, Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids, European Mathematical Society, Tracts in Mathematics. 15 (2011). https://doi.org/10.4171/083
- R. Brown, J. Huebschmann, Identities among relations, in Low Dimentional Topology, London Math. Soc. Lect. Notes, Cambridge Univ. Press. 48 (1982), 153-202. https://doi.org/10.1017/CBO9780511758935.010
- C. Ehresmann, Categories doubles et categories structures, C. R. Acad. Sci. Paris. 256 (1963) 1198-1201.
- M.R. Farhangdoost, T. Nasirzade, Geometrical categories of generalized Lie groups and Lie group-groupoids, Iran J. Sci Technol A. (2013), 69-73. https://www.researchgate.net/publication/267660211_Geometrical_Categories_of_Generalized_Lie_Groups_and_Lie_Group-Groupoids
- M. H. Gursoy, H. Aslan, I, Icen, Generalized crossed modules and group-groupoids, Turkish Journal of Mathematics. 41 (2017), 1535-1551. https://doi.org/10.3906/mat-1602-63
- J. Huebschmann, Crossed n-fold extensions of groups and cohomology, Comment. Math. Helvetici. 55 (1980), 302-314. https://doi.org/10.1007/BF02566688
- J. L. Loday, Cohomologie et groupes de Steinberg relatifs, J. Algebra. 54 (1978) 178-202. https://doi.org/10.1016/0021-8693(78)90025-X
- A. S. T. Lue, Cohomology of groups relative to a variety, J. Algebra. 69 (1981), 155-174, . https://doi.org/10.1016/0021-8693(81)90136-8
- M. Mehrabi, M.R. Molaei, A. Olomi, Generalized subgroups and homomorphisms, Arab J Math Sci. 6 (2000) 1-7. https://ajms.ksu.edu.sa/sites/ajms.ksu.edu.sa/files/imce_images/1._m._mehrabi_m._r._molaei_and_a._oloomi.pdf
- M.R. Molaei, Generalized groups, Bul Inst Politeh Iasi Sect I Mat Mec Teor Fiz. 45 (1999), 21-24.
- M.R. Molaei, Generalized action, In: Mladenov IM, Naber GL, editors, International Conference on Geometry, Integrability and Quantization, September (1999) 1-10 ;Varna, Bulgaria. Sofia: Coral Press. (1999), 175-179. https://doi.org/10.7546/giq-1-2000-175-179
- O. Mucuk, H.F. Akiz, Monodromy groupoid of an internal groupoid in topological groups with operations, Filomat. 29 (10) (2015), 2355-2366. https://doi.org/10.2298/FIL1510355M
- O. Mucuk , T. Sahan, N. Alemdar, Normality and Quotients in Crossed Modules and Group-groupoids, Applied Categorical Structures. 23 (2015), no.3 415-428. https://doi.org/10.1007/s10485-013-9335-6
- T. Porter, Extensions, crossed modules and internal categories in categories of groups with operations, Proc. Edinb. Math. Soc. 30 (1987) 373-381. https://doi.org/10.1017/S0013091500026766
- S. Temel, T. Sahan, O. Mucuk, Crossed Modules, Double Group-Grouoids and Crossed Squares, Filomat. 34 (6) (2020), 1755-1769. https://doi.org/10.2298/FIL2006755T
- J. H. C. Whitehead, Note on a previous paper entitled,On adding relations to homotopy group, Ann. of Math. 47 (2) (1946), 806-810 https://doi.org/10.2307/1969237
- J. H. C. Whitehead, Combinatorial homotopy II, Bull. Amer. Math. Soc. 55 (1949), 453-496. https://doi.org/10.1090/S0002-9904-1949-09213-3