Journals / Mathematical Sciences and Applications E-Notes / 2020 / Cilt: 8 - Sayı: 1

Some Remarks on MCI Crossed Modules

Pages
193–201
Publication Date
2022-10-19
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Inthis paper, we prove that this is also true without any restriction.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
💡
Conclusion & Impact:Inthis paper, we prove that this is also true without any restriction.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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. Inthis paper, we prove that this is also true without any restriction.

🔖

Cite This Article

EMİR, K. (2022). Some Remarks on MCI Crossed Modules. Mathematical Sciences and Applications E-Notes, Cilt: 8 - Sayı: 1, 193–201. https://ajindex.com/articles/578819

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (17)

  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, ˙I.: 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., ¸Sahan, 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).