| 三角范畴和Abel范畴的Torsion理论 |
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| 引用本文： | 林记,姚云飞.三角范畴和Abel范畴的Torsion理论[J].数学杂志,2014,34(6):1134-1140. |
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| 作者姓名： | 林记 姚云飞 |
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| 作者单位： | 阜阳师范学院数学与计算科学学院; |
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| 基金项目： | 国家级特色专业“数学与应用数学”建设项目(TS11496);阜阳师范学院精品开放课程(2012KFKC10);阜阳师范学院自然科学研究项目(2013FSKJ07);阜阳师范学院自然科学研究项目(2013FSKJ13);安徽省高等学校优秀青年人才基金项目(2012SQRL115ZD)资助 |
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| 摘 要： | 本文主要研究了三角范畴在Abel化过程中torsion理论的保持问题.利用三角范畴的coherent函子范畴是Abel范畴,证明了T的coherent函子范畴A(T)是A(D)的thick子范畴;若(X,Y)是D的torsion理论,且D=X*Y的扩张是可裂的,那么(A(X),A(Y))是A(D)的torsion理论.
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| 关 键 词： | 三角范畴 coherent函子范畴 thick子范畴 torsion理论 |
| 收稿时间： | 2013/10/8 0:00:00 |
| 修稿时间： | 2013/12/3 0:00:00 |
TORSION THEORY OF TRIANGULATED CATEGORIES AND ABELIAN CATEGORIES |
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| LIN Ji and YAO Yun-fei.TORSION THEORY OF TRIANGULATED CATEGORIES AND ABELIAN CATEGORIES[J].Journal of Mathematics,2014,34(6):1134-1140. |
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| Authors: | LIN Ji and YAO Yun-fei |
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| Affiliation: | School of Mathematics and Computational Science, Fuyang Teachers College, Fuyang 236037, China and School of Mathematics and Computational Science, Fuyang Teachers College, Fuyang 236037, China |
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| Abstract: | The preserving problems of torsion theory during the course of the Abelianization of triangulated categories are studied. By using the conclusion that the coherent functor category of triangulated category is an Abelian category, it is shown that the coherent functor category A(T) of T is a thick subcategory of A(D). If (X, Y) is a torsion theory of D and the extension of X by Y is split, we prove that (A(X),A(Y)) is a torsion theory of A(D). |
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| Keywords: | triangulated category coherent functor category thick subcategory torsion theory |
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