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Colimits of crossed modules in modified categories of interest

  • Received: 01 April 2020 Revised: 01 May 2020
  • Primary: 17A30; Secondary: 18G45, 18A30

  • In this paper, we give the constructions of the coequalizer and coproduct objects for the category of crossed modules, in a modified category of interest (MCI). In other words, we prove that the corresponding category is finitely cocomplete.

    Citation: Ali Aytekin, Kadir Emir. Colimits of crossed modules in modified categories of interest[J]. Electronic Research Archive, 2020, 28(3): 1227-1238. doi: 10.3934/era.2020067

    Related Papers:

  • In this paper, we give the constructions of the coequalizer and coproduct objects for the category of crossed modules, in a modified category of interest (MCI). In other words, we prove that the corresponding category is finitely cocomplete.



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    [1] Pullbacks of crossed modules and cat1-groups. Turkish J. Math. (1998) 22: 273-281.
    [2] Pullbacks of crossed modules and Cat1-commutative algebras. Turkish J. Math. (2006) 30: 237-246.
    [3] Pullback and pushout crossed polymodules. Proc. Indian Acad. Sci., Math. Sci. (2015) 125: 11-20.
    [4] Actions in modified categories of interest with application to crossed modules. Theory Appl. Categ. (2015) 30: 882-908.
    [5] Coproducts of crossed $P$-modules: Applications to second homotopy groups and to the homology of groups. Topology (1984) 23: 337-345.
    [6] From groups to groupoids: A brief survey. Bull. Lond. Math. Soc. (1987) 19: 113-134.
    [7] Modelling and computing homotopy types: I. Indag. Math. (N.S.) (2018) 29: 459-482.
    [8] On finite induced crossed modules and the homotopy $2$-type of mapping cones. Theory Appl. Categ. (1995) 1: 54-70.
    [9] J. M. Casas, R. F. Casado, E. Khmaladze and M. Ladra, More on crossed modules in Lie, Leibniz, associative and diassociative algebras, J. Algebra Appl., 16 (2017), 1750107, 17 pp. doi: 10.1142/S0219498817501079
    [10] J. Casas, T. Datuashvili and M. Ladra, Actors in categories of interest, arXiv: math/0702574.
    [11] Universal strict general actors and actors in categories of interest. Appl. Categ. Struct. (2010) 18: 85-114.
    [12] Colimits in the crossed modules category in Lie algebras. Georgian Math. J. (2000) 7: 461-474.
    [13] Limits in modified categories of interest. Bull. Iran. Math. Soc. (2017) 43: 2617-2634.
    [14] Pullback crossed modules in the category of racks. Hacet. J. Math. Stat. (2019) 48: 140-149.
    [15] Groups with multiple operators. Proc. Lond. Math. Soc. (1956) 6: 366-416.
    [16] Spaces with finitely many non-trivial homotopy groups. J. Pure Appl. Algebra (1982) 24: 179-202.
    [17] On the $3$-type of a complex. Proc. Natl. Acad. Sci. U.S.A. (1950) 36: 41-48.
    [18] Obstruction theory in algebraic categories. I. J. Pure Appl. Algebra (1972) 2: 287-314.
    [19] Extensions, crossed modules and internal categories in categories of groups with operations. Proc. Edinb. Math. Soc. (1987) 30: 373-381.
    [20] N. Shammu, Algebraic and Categorical Structure of Categories of Crossed Modules of Algebras, University College of North Wales, 1992.
    [21] Combinatorial homotopy. II. Bull. Amer. Math. Soc. (1949) 55: 453-496.
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