On morphisms of crossed polymodules
الموضوعات :
1 - Department of Mathematics, Yazd University, Yazd, Iran
2 - Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic
الکلمات المفتاحية: Limit, Polygroup, crossed module,
ملخص المقالة :
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.
[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.
