RELATIONS AMONG HIGHER ORDER CROSSED MODULES OVER GROUPOIDS

Year 2016, Volume: 4 Issue: 1, 282 - 290, 01.04.2016

Çağri Ataseven

https://izlik.org/JA88LD29KH

Abstract

In this work, we explored the categorical relationships between crossed modules, 2-and 3- crossed modules of groupoids

Keywords

Crossed modules , 2-crossed modules , Groupoids

References

• [1] Arvasi, Z., Ulualan, E., On Algebraic Models for Homotopy 3-Types, Journal of Homotopy and Related Structures, vol. 1(1),2006,pp 1-27.
• [2] Arvasi, Z., Kuzpinari, T.S., Uslu, E.O., 3-crossed modules, Homology Homotopy and Applications, 11, 2, 161- 187, (2009).
• [3] Brown, R., Possible connections between whiskered categories and groupoids leibniz algebras automorphism structure and local-to-global questions, Journal of Homotopy and Related Structures, 5, 1, 308-318, (2010).
• [4] Brown, R., From groups to groupoids, Bull. London Math Soc., 19, 1, 113-134, (1987).
• [5] Brown, R., Gilbert, N.D., Algebraic models of 3-types and automorphism structures for crossed modules, Proc. London Math Soc., 3, 51-73,(1989).
• [6] Brown, R., Higgins, P.J., On the algebra of cubes, Journal of Pure and Applied Algebra, 21, 233-260,(1981).
• [7] Brown, R., Spencer, C.B., G-groupoids, crossed modules and fundamental groupoid of a topological group, Proc. Konink. Neder. Akad. Van Wetenschappen Amsterdam, 79, 4,(1976).
• [8] Conduche, D., Modules croises generalises de longuer 2, Journal of Pure and Applied Algebra, 34, 155-178, (1984).
• [9] Loday, J.L., Spaces with nitely many non-trival homotopy groups, Journal of Pure and Applied Algebra, 24, 179-202, (1982).
• [10] Ulualan, E., Pak, S., Braiding for internal categories in the category of whiskered groupoids and simplicial groups, Turk J Math ,37 , 145-164,(2013).
• [11] Whitehead, J.H.C., Combinatorial homotopy II, Bull. Amer. Math. Soc., 55, 453-496, (1949).