Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 8 Sayı: 1, 193 - 201, 20.03.2020
https://doi.org/10.36753/mathenot.602513

Öz

Kaynakça

  • [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

Yıl 2020, Cilt: 8 Sayı: 1, 193 - 201, 20.03.2020
https://doi.org/10.36753/mathenot.602513

Öz

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.

Destekleyen Kurum

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).

Kaynakça

  • [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).
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Kadir Emir 0000-0003-4369-3508

Yayımlanma Tarihi 20 Mart 2020
Gönderilme Tarihi 6 Ağustos 2019
Kabul Tarihi 23 Mart 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 1

Kaynak Göster

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. Mart 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, sy. 1 (Mart 2020): 193-201. https://doi.org/10.36753/mathenot.602513.
EndNote Emir K (01 Mart 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, c. 8, sy. 1, ss. 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 (Mart 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, c. 8, sy. 1, 2020, ss. 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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