ON THE CATEGORY OF U-COMPLEXES AND THE CATEGORY OF WEAKLY U-COMPLEXES - Elfiyanti, Gustina
In 2002, Davvaz and Shabani-Solt introduced chain U-complexes as a generalization of the chain complexes of R-modules. They established some results in homological algebra such as Lambek Lemma, Snake Lemma, Connecting homomorphism and Exact Triangle. One of the interesting topics related to chain complexes of is the category of complexes of R-modules. This category is introduced in representation theory because the categories of modules over an algebra is considerd insufficient in some situations. The category of complexes is abelian and the homotopy category of complexes is triangulated. Hence, the derived category of complexes can be constructed from these categories. In this dissertation, some results by Davvaz and Shabani-Solt’s are used to define the category of U-complexes and study its structure. We prove that both of the category of U-complexes is abelian and the homotopy category of U-complexes is additive. In this dissertation we also introduce the notion of weakly chain U-complexes by replacing the second condition of chain U-complexes. Then, we study the category of weakly U-complexes. We show that the category of weakly U-complexes is an additive category and the homotopy category of U-complexes is a triangulated category. Hopefully, we can construct the derived category of weakly U-complexes