ON THE CATEGORY OF U-COMPLEXES AND THE CATEGORY OF WEAKLY U-COMPLEXES
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 chai...
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id-itb.:519652021-01-05T09:23:48ZON THE CATEGORY OF U-COMPLEXES AND THE CATEGORY OF WEAKLY U-COMPLEXES Elfiyanti, Gustina Indonesia Dissertations category of U-complexes, category homotopy of U-complexes, category of weakly U-complexes, category homotopy of weakly U-complexes, additive category, triangulated category. INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/51965 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 text |
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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 |
| format |
Dissertations |
| author |
Elfiyanti, Gustina |
| spellingShingle |
Elfiyanti, Gustina ON THE CATEGORY OF U-COMPLEXES AND THE CATEGORY OF WEAKLY U-COMPLEXES |
| author_facet |
Elfiyanti, Gustina |
| author_sort |
Elfiyanti, Gustina |
| title |
ON THE CATEGORY OF U-COMPLEXES AND THE CATEGORY OF WEAKLY U-COMPLEXES |
| title_short |
ON THE CATEGORY OF U-COMPLEXES AND THE CATEGORY OF WEAKLY U-COMPLEXES |
| title_full |
ON THE CATEGORY OF U-COMPLEXES AND THE CATEGORY OF WEAKLY U-COMPLEXES |
| title_fullStr |
ON THE CATEGORY OF U-COMPLEXES AND THE CATEGORY OF WEAKLY U-COMPLEXES |
| title_full_unstemmed |
ON THE CATEGORY OF U-COMPLEXES AND THE CATEGORY OF WEAKLY U-COMPLEXES |
| title_sort |
on the category of u-complexes and the category of weakly u-complexes |
| url |
https://digilib.itb.ac.id/gdl/view/51965 |
| _version_ |
1822272924075163648 |