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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. |
| 关键词: 三角范畴 coherent函子范畴 thick子范畴 torsion理论 |
| DOI： |
| 分类号:O154.1 |
| 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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| TORSION THEORY OF TRIANGULATED CATEGORIES AND ABELIAN CATEGORIES |
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LIN Ji,YAO Yun-fei
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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). |
| Key words: triangulated category coherent functor category thick subcategory torsion theory |
