On the Category of Weakly U-Complexes

Authors

  • Gustina Elfiyanti Universitas Islam Negeri Syarif Hidayatullah Jakarta, Indonesia
  • Intan Muchtadi-Alamsyah Institut Teknologi Bandung
  • Fajar Yuliawan Institut Teknologi Bandung
  • Dellavitha Nasution Institut Teknologi Bandung

DOI:

https://doi.org/10.29020/nybg.ejpam.v13i2.3673

Keywords:

$\mathcal{U}$-complexes, generalized $\mathcal{U}$-complexes, homotopy category of generalized $\mathcal{U}$-complexes, triangulated category

Abstract

Motivated by a study of Davvaz and Shabbani which introduced the concept of U-
complexes and proposed a generalization on some results in homological algebra, we study thecategory of U-complexes and the homotopy category of U-complexes. In [8] we said that the category of U-complexes is an abelian category. Here, we show that the object that we claimed to be the kernel of a morphism of U-omplexes does not satisfy the universal property of the kernel, hence wecan not conclude that the category of U-complexes is an abelian category. The homotopy category of U-complexes is an additive category. In this paper, we propose a weakly chain U-complex by changing the second condition of the chain U-complex. We prove that the homotopy category ofweakly U-complexes is a triangulated category.

Author Biographies

  • Gustina Elfiyanti, Universitas Islam Negeri Syarif Hidayatullah Jakarta, Indonesia
    Department of Mathematics, Faculty of Science and Technology
  • Intan Muchtadi-Alamsyah, Institut Teknologi Bandung
    Algebra Research Group, Faculty of Natural Sciences and Mathematics
  • Fajar Yuliawan, Institut Teknologi Bandung
    Algebra Research Group, Faculty of Natural Sciences and Mathematics
  • Dellavitha Nasution, Institut Teknologi Bandung
    Algebra Research Group, Faculty of Natural Sciences and Mathematics

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Published

2020-04-29

Issue

Section

Nonlinear Analysis

How to Cite

On the Category of Weakly U-Complexes. (2020). European Journal of Pure and Applied Mathematics, 13(2), 323-345. https://doi.org/10.29020/nybg.ejpam.v13i2.3673