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Research Article

On classifying simplicial modules

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Pages 945-959 | Received 28 Sep 2022, Accepted 30 Aug 2023, Published online: 12 Sep 2023

References

  • Arvasi, Z., Porter, T. (1997). Higher dimensional peiffer elements in simplicial commutative algebras. Theory Appl. Categories 3:1–23.
  • Arvasi, Z., Porter, T. (1998). Freeness conditions for 2-crossed modules of commutative algebras. Appl. Categorical Struct. 6:455–471.
  • Brown, R., Loday, J. L. (1987). Van-Kampen theorems for diagram of spaces. Topology 26:311–335. DOI: 10.1016/0040-9383(87)90004-8.
  • Carrasco, P., Cegarra, A. M., Grandjean, A. R. (2002). (Co)Homology of crossed modules. J. Pure Appl. Algebra 168:147–176. DOI: 10.1016/S0022-4049(01)00094-9.
  • Cegarra, A. M., Remedios, J. (2005). The relationship between the diagonal and the bar constructions on a bisimplicial set. Topol. Appl. 153(1):21–51. DOI: 10.1016/j.topol.2004.12.003.
  • Curtis, E. B. (1971). Simplicial homotopy theory. Adv. Math. 6:107–209. DOI: 10.1016/0001-8708(71)90015-6.
  • Ellis, G. J. (1992). Homology of 2-types. J. London Math. Soc. 46:1–27. DOI: 10.1112/jlms/s2-46.1.1.
  • Ellis, G. J., Luyen, L. V. (2012). Computational homology of n-types. J. Symb. Comput. 47:1309–1317. DOI: 10.1016/j.jsc.2012.02.003.
  • Ellis, G. J., Luyen, L. V. (2014). Homotopy 2-types of low order. J. Exp. Math. 23:383–389. DOI: 10.1080/10586458.2014.912059.
  • Grandjean, A. R., Ladra, M., Pirashvili, T. (2000). CCG-homology of crossed modules via classifying spaces. J. Algebra 229:660–665. DOI: 10.1006/jabr.2000.8296.
  • Goerss, P. G., Jardine, J. F. (1999). Simplicial Homotopy Theory. Progress in Mathematics, Vol. 174. Basel-Boston-Berlin: Birkhauser.
  • Ilgaz, E. (2018) (Co)Homology of crossed modules of algebras. PhD. Eskişehir Osmangazi University, Turkey.
  • Kan, D. M. (1958) On homotopy theory and css groups. Ann. Math. 68:38–53. DOI: 10.2307/1970042.
  • May, J. P. (1967). Simplicial Objects in Algebraic Topology. Mathematic Studies, Vol. 11. Princeton: Van Nostrand.
  • Paoli, S. (2003) (Co)Homology of crossed modules with coefficients in a π1-module. Homol. Homotopy Appl. 5(1):261–296. DOI: 10.4310/HHA.2003.v5.n1.a12.
  • Thomas, S. (2008). The functors W¯ and Diag°Nerve are simplicially homotopy equivalent. J. Homotopy Relat. Struct. 3(1):359–378.
  • Porter, T. (1986). Homology of commutative algebras and an invariant of Simis and Vasconceles. J. Algebra 99: 458–465. DOI: 10.1016/0021-8693(86)90038-4.
  • Porter, T. (1987). Some categorical results in the theory of crossed modules in commutative algebras. J. Algebra, 109:415–429. DOI: 10.1016/0021-8693(87)90147-5.
  • Porter, T. (2011). The crossed menagerie. http://ncatlab.org/timporter/files/menagerie11.pdf.
  • Whitehead, J. H. C. (1949). Combinatorial homotopy I-II. Bull. Amer. Math. Soc. 55:213–245, 453–496. DOI: 10.1090/S0002-9904-1949-09213-3.

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