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Year 2020, Volume: 8 Issue: 1, 193 - 201, 20.03.2020
https://doi.org/10.36753/mathenot.602513

Abstract

References

  • [1] Alp, M., Davvaz, M.: Crossed polymodules and fundamental relations. Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar., 77(2):129–140 (2015).
  • [2] Aytekin, A., Casas, J.M., Uslu, E. Ö.: Semi-complete crossed modules of Lie algebras. J. Algebra Appl., 11(5):1250096, 24 (2012).
  • [3] Aytekin, A., Emir, K.: Colimits of crossed modules in modified categories of interest. Preprint.
  • [4] Boyaci, Y., Casas, J.M., Datuashvili, T., Uslu, E.Ö.: Actions in modified categories of interest with application to crossed modules. Theory Appl. Categ., 30:882–908 (2015).
  • [5] Brown, R.: Modelling and computing homotopy types: I. Indag. Math., New Ser., 29(1):459–482 (2018).
  • [6] Casas, J.M., Casado, R.F., Khmaladze, E., Ladra, M.: More on crossed modules in Lie, Leibniz, associative and diassociative algebras. J. Algebra Appl., 16(6):17 (2017).
  • [7] Crans, A.S., Wagemann, F.: Crossed modules of racks. Homology Homotopy Appl., 16(2):85–106 (2014).
  • [8] Emir, K., Çetin, S.: Limits in modified categories of interest. Bull. Iran. Math. Soc., 43(7):2617–2634 (2017).
  • [9] Emir, K., Gülsün Akay, H.: Pullback crossed modules in the category of racks. Hacet. J. Math. Stat., 48(1):140–149 (2019).
  • [10] Faria Martins, J.: Crossed modules of Hopf algebras and of associative algebras and two-dimensional holonomy. J. Geom. Phys., 99:68–110 (2016).
  • [11] Gülsün Akay, H., Akça, İ.: Completeness of the category of rack crossed modules. Preprint.
  • [12] Higgins, P.J.: Groups with multiple operators. Proc. Lond. Math. Soc. (3), 6:366–416 (1956).
  • [13] Mucuk, O., Şahan, T.: Group-groupoid actions and liftings of crossed modules. Georgian Math. J., 26(3):437–447 (2019).
  • [14] Orzech, G.: Obstruction theory in algebraic categories. I-II. J. Pure Appl. Algebra, 2:287–340 (1972).
  • [15] Porter, T.: Extensions, crossed modules and internal categories in categories of groups with operations. Proc. Edinb. Math. Soc., II. Ser., 30:373–381 (1987).
  • [16] Whitehead, J.H.C.: On adding relations to homotopy groups. Ann. of Math. (2) (1941).
  • [17] Yavari, M., Salemkar, A.: The category of generalized crossed modules. Categ. Gen. Algebr. Struct. Appl. 10(1):157– 171 (2019).

Some Remarks on MCI Crossed Modules

Year 2020, Volume: 8 Issue: 1, 193 - 201, 20.03.2020
https://doi.org/10.36753/mathenot.602513

Abstract

In an earlier work, it is proven that the category of crossed modules in a modified category of interest
(MCI crossed modules) is finitely complete with a certain condition, in which all codomains are fixed. In
this paper, we prove that this is also true without any restriction.

Supporting Institution

The author was supported by the projects Mathematical Structures 9 (MUNI/A/0885/2019), and Group Techniques and Quantum Information (MUNI/G/1211/2017) by Masaryk University Grant Agency (GAMU).

References

  • [1] Alp, M., Davvaz, M.: Crossed polymodules and fundamental relations. Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar., 77(2):129–140 (2015).
  • [2] Aytekin, A., Casas, J.M., Uslu, E. Ö.: Semi-complete crossed modules of Lie algebras. J. Algebra Appl., 11(5):1250096, 24 (2012).
  • [3] Aytekin, A., Emir, K.: Colimits of crossed modules in modified categories of interest. Preprint.
  • [4] Boyaci, Y., Casas, J.M., Datuashvili, T., Uslu, E.Ö.: Actions in modified categories of interest with application to crossed modules. Theory Appl. Categ., 30:882–908 (2015).
  • [5] Brown, R.: Modelling and computing homotopy types: I. Indag. Math., New Ser., 29(1):459–482 (2018).
  • [6] Casas, J.M., Casado, R.F., Khmaladze, E., Ladra, M.: More on crossed modules in Lie, Leibniz, associative and diassociative algebras. J. Algebra Appl., 16(6):17 (2017).
  • [7] Crans, A.S., Wagemann, F.: Crossed modules of racks. Homology Homotopy Appl., 16(2):85–106 (2014).
  • [8] Emir, K., Çetin, S.: Limits in modified categories of interest. Bull. Iran. Math. Soc., 43(7):2617–2634 (2017).
  • [9] Emir, K., Gülsün Akay, H.: Pullback crossed modules in the category of racks. Hacet. J. Math. Stat., 48(1):140–149 (2019).
  • [10] Faria Martins, J.: Crossed modules of Hopf algebras and of associative algebras and two-dimensional holonomy. J. Geom. Phys., 99:68–110 (2016).
  • [11] Gülsün Akay, H., Akça, İ.: Completeness of the category of rack crossed modules. Preprint.
  • [12] Higgins, P.J.: Groups with multiple operators. Proc. Lond. Math. Soc. (3), 6:366–416 (1956).
  • [13] Mucuk, O., Şahan, T.: Group-groupoid actions and liftings of crossed modules. Georgian Math. J., 26(3):437–447 (2019).
  • [14] Orzech, G.: Obstruction theory in algebraic categories. I-II. J. Pure Appl. Algebra, 2:287–340 (1972).
  • [15] Porter, T.: Extensions, crossed modules and internal categories in categories of groups with operations. Proc. Edinb. Math. Soc., II. Ser., 30:373–381 (1987).
  • [16] Whitehead, J.H.C.: On adding relations to homotopy groups. Ann. of Math. (2) (1941).
  • [17] Yavari, M., Salemkar, A.: The category of generalized crossed modules. Categ. Gen. Algebr. Struct. Appl. 10(1):157– 171 (2019).
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Kadir Emir 0000-0003-4369-3508

Publication Date March 20, 2020
Submission Date August 6, 2019
Acceptance Date March 23, 2020
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

APA Emir, K. (2020). Some Remarks on MCI Crossed Modules. Mathematical Sciences and Applications E-Notes, 8(1), 193-201. https://doi.org/10.36753/mathenot.602513
AMA Emir K. Some Remarks on MCI Crossed Modules. Math. Sci. Appl. E-Notes. March 2020;8(1):193-201. doi:10.36753/mathenot.602513
Chicago Emir, Kadir. “Some Remarks on MCI Crossed Modules”. Mathematical Sciences and Applications E-Notes 8, no. 1 (March 2020): 193-201. https://doi.org/10.36753/mathenot.602513.
EndNote Emir K (March 1, 2020) Some Remarks on MCI Crossed Modules. Mathematical Sciences and Applications E-Notes 8 1 193–201.
IEEE K. Emir, “Some Remarks on MCI Crossed Modules”, Math. Sci. Appl. E-Notes, vol. 8, no. 1, pp. 193–201, 2020, doi: 10.36753/mathenot.602513.
ISNAD Emir, Kadir. “Some Remarks on MCI Crossed Modules”. Mathematical Sciences and Applications E-Notes 8/1 (March 2020), 193-201. https://doi.org/10.36753/mathenot.602513.
JAMA Emir K. Some Remarks on MCI Crossed Modules. Math. Sci. Appl. E-Notes. 2020;8:193–201.
MLA Emir, Kadir. “Some Remarks on MCI Crossed Modules”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, 2020, pp. 193-01, doi:10.36753/mathenot.602513.
Vancouver Emir K. Some Remarks on MCI Crossed Modules. Math. Sci. Appl. E-Notes. 2020;8(1):193-201.

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