On the Category of Weakly U-Complexes

Gustina Elfiyanti, Intan Muchtadi-Alamsyah, Fajar Yuliawan, Dellavitha Nasution

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.

Keywords

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

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