Document Type: Research Paper

Authors

1 Department of Mathematics‎, ‎Yazd University‎, ‎Yazd‎, ‎Iran

2 Department of Mathematics and Statistics‎, ‎Masaryk University‎, ‎Brno‎, ‎Czech Republic

Abstract

‎In this paper‎, ‎we prove that the category of crossed polymodules (i.e‎. ‎crossed modules of polygroups) and their morphisms is finitely complete‎. ‎We‎, ‎therefore‎, ‎generalize the group theoretical case of this completeness property of crossed modules‎.

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Main Subjects

[1] M. Alp, B. Davvaz, Crossed polymodules and fundamental relations, U.P.B. Sci. Bull. (Series A). 77 (1) (2015), 129–140.
[2] S. Awodey, Category Theory, Oxford: Oxford University Press, 2006.
[3] R. Brown, From groups to groupoids: A brief survey, Bull. Lond. Math. Soc. 19 (1987), 113–134.
[4] R. Brown, Modelling and computing homotopy types: I, Indag. Math. 29 (1) (2018) 459–482.
[5] S. D. Comer, Polygroups derived from cogroups, Journal of Algebra. 89 (2) (1984), 397 – 405.
[6] B. Davvaz, On polygroups and permutation polygroups, Math. Balkanica. 14 (1-2) (2000), 41–58.
[7] B. Davvaz, Polygroup Theory and Related Systems, World Scientific, 2012.
[8] B. Davvaz, M. Alp, Derivation and actor of crossed polymodules, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 25 (3) (2018), 203-218.
[9] B. Davvaz, T. Vougiouklis, A walk through weak hyperstructures. Hv-structures, Hackensack, NJ: World Scientific, 2019.
[10] K. Emir, S. C ¸etin, Limits in modified categories of interest, Bull. Iran. Math. Soc. 43 (7) (2017), 2617-2634.
[11] J. Faria Martins, R. Picken, On two-dimensional holonomy, Trans. Am. Math. Soc. 362 (11) (2010), 5657-5695.
[12] S. N. Hosseini, S. S. Mousavi, M. M. Zahedi, Category of polygroup objects, Bull. Iran. Math. Soc. 28 (1) (2002), 67-86.
[13] J. C. Morton, R. Picken, Transformation double categories associated to 2-group actions, Theory Appl. Categ. 30 (2015), 1429-1468.
[14] J. Whitehead, On adding relations to homotopy groups, Ann. Math. 42 (2) (1941), 409-428.
[15] M. Yavari, A. Salemkar, The category of generalized crossed modules, Categ. Gen. Algebr. Struct. Appl. 10 (1) (2019), 157-171.