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Generalized crossed modules over generalized group-groupoids

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In this paper we define generalized double group-groupoids and crossed modules over generalized group-groupoids. Also we prove that these algebraic structures are categorically equivalent.

Abstract

In this paper we define generalized double group-groupoids and crossed modules over generalized group-groupoids. Also we prove that these algebraic structures are categorically equivalent.

참고문헌 (26)

  1. S. A Ahmadi, "Generalized topological groups and genetic recombination", J Dyn Syst Geom Theor, 11, pp.51~58 (2013)[DOI]
  2. H. F. Akꠕz, "Coverings of internal groupoids and crossed modules in the category of groups with operations", Georgian Math. Journal, 20(2), pp.223~238 (2013)[DOI]
  3. J.T.Akinmoyewa, "A study of some properties of generalized groups", Octogon Mathematical Magazine, 17, pp.125~134 (2009)
  4. J. C. Baez, "Higher-dimensional algebra V : 2-groups", Theory Appl. Categ, 12, pp.423~491 (2004)[DOI]
  5. R. Brown, "Topology and groupoids" (2006), Booksurge PLC
  6. R. Brown, "Low Dimensional Topology", pp.215~238 (1982), Cambridge Univ. Press
  7. R. Brown, "Covering groups of non-connected topological groups revisited", Math. Proc. Camb. Phill. Soc, 115, pp.97~110 (1994)[DOI]
  8. R. Brown, "G-groupoids, crossed modules and the fundamental groupoid of a topo-logical group", Proc. Konn. Ned. Akad. v. Wet, 79, pp.296~302 (1976)[DOI]
  9. R. Brown, "Double groupoids and crossed modules", Cah. Topol. Geom. Dier. Categ, 17, pp.343~362 (1976)
  10. R. Brown, "Nonabelian algebraic topology: ltered spaces, crossed com-plexes, cubical homotopy groupoids", European Mathematical Society, Tracts in Mathematics, 15 (2011)[DOI]
  11. R. Brown, "Low Dimentional Topology", pp.153~202 (1982), Cambridge Univ. Press
  12. C. Ehresmann, "Categories doubles et categories structures", C. R. Acad. Sci. Paris, 256, pp.1198~1201 (1963)
  13. M.R. Farhangdoost, "Geometrical categories of generalized Lie groups and Lie group-groupoids", Iran J. Sci Technol A, pp.69~73 (2013)
  14. M. H. Gursoy, "Generalized crossed modules and group-groupoids", Turkish Journal of Mathematics, 41, pp.1535~1551 (2017)[DOI]
  15. J. Huebschmann, "Crossed n-fold extensions of groups and cohomology", Comment. Math. Helvetici, 55, pp.302~314 (1980)[DOI]
  16. J. L. Loday, "Cohomologie et groupes de Steinberg relatifs", J. Algebra, 54, pp.178~202 (1978)[DOI]
  17. A. S. T. Lue, "Cohomology of groups relative to a variety", J. Algebra, 69, pp.155~174 (1981)[DOI]
  18. M. Mehrabi, "Generalized subgroups and homomorphisms", Arab J Math Sci, 6, pp.1~7 (2000)
  19. M. R. Molaei, "Generalized groups", Bul Inst Politeh Iasi Sect I Mat Mec Teor Fiz, 45, pp.21~24 (1999)
  20. M. R. Molaei, "International Conference on Geometry, Integrability and Quantization", pp.175~179 (1999), Coral Press
  21. O. Mucuk, "Monodromy groupoid of an internal groupoid in topological groups with operations", Filomat, 29(10), pp.2355~2366 (2015)[DOI]
  22. O. Mucuk, "Normality and Quotients in Crossed Modules and Group-groupoids", Applied Categorical Structures, 23(3), pp.415~428 (2015)[DOI]
  23. T. Porter, "Extensions, crossed modules and internal categories in categories of groups with operations", Proc. Edinb. Math. Soc, 30, pp.373~381 (1987)[DOI]
  24. S. Temel, "Crossed Modules, Double Group-Grouoids and Crossed Squares", Filomat, 34(6), pp.1755~1769 (2020)[DOI]
  25. J. H. C. Whitehead, "Note on a previous paper entitled,On adding relations to homotopy group", Ann. of Math, 47(2), pp.806~810 (1946)[DOI]
  26. J. H. C. Whitehead, "Combinatorial homotopy II", Bull. Amer. Math. Soc, 55, pp.453~496 (1949)

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