Research Article

Some Remarks on MCI Crossed Modules

Volume: 8 Number: 1 March 20, 2020
EN

Some Remarks on MCI Crossed Modules

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.

Keywords

modified category of interest,crossed module,limit

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. [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. [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. [3] Aytekin, A., Emir, K.: Colimits of crossed modules in modified categories of interest. Preprint.
  4. [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. [5] Brown, R.: Modelling and computing homotopy types: I. Indag. Math., New Ser., 29(1):459–482 (2018).
  6. [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. [7] Crans, A.S., Wagemann, F.: Crossed modules of racks. Homology Homotopy Appl., 16(2):85–106 (2014).
  8. [8] Emir, K., Çetin, S.: Limits in modified categories of interest. Bull. Iran. Math. Soc., 43(7):2617–2634 (2017).
  9. [9] Emir, K., Gülsün Akay, H.: Pullback crossed modules in the category of racks. Hacet. J. Math. Stat., 48(1):140–149 (2019).
  10. [10] Faria Martins, J.: Crossed modules of Hopf algebras and of associative algebras and two-dimensional holonomy. J. Geom. Phys., 99:68–110 (2016).
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
1.Emir K. Some Remarks on MCI Crossed Modules. Math. Sci. Appl. E-Notes. 2020;8(1):193-201. doi:10.36753/mathenot.602513
Chicago
Emir, Kadir. 2020. “Some Remarks on MCI Crossed Modules”. Mathematical Sciences and Applications E-Notes 8 (1): 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
[1]K. Emir, “Some Remarks on MCI Crossed Modules”, Math. Sci. Appl. E-Notes, vol. 8, no. 1, pp. 193–201, Mar. 2020, doi: 10.36753/mathenot.602513.
ISNAD
Emir, Kadir. “Some Remarks on MCI Crossed Modules”. Mathematical Sciences and Applications E-Notes 8/1 (March 1, 2020): 193-201. https://doi.org/10.36753/mathenot.602513.
JAMA
1.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, Mar. 2020, pp. 193-01, doi:10.36753/mathenot.602513.
Vancouver
1.Kadir Emir. Some Remarks on MCI Crossed Modules. Math. Sci. Appl. E-Notes. 2020 Mar. 1;8(1):193-201. doi:10.36753/mathenot.602513