| 三角范畴的Recollement与Abel化 |
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| 引用本文： | 唐丽丹,陈清华.三角范畴的Recollement与Abel化[J].莆田高等专科学校学报,2012(5):1-4,13. |
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| 作者姓名： | 唐丽丹 陈清华 |
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| 作者单位： | [1]福州大学数学与计算机科学学院,福建福州350108 [2]福建师范大学数学与计算机科学学院,福建福州350007 |
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| 基金项目： | 国家自然科学基金资助项目（11126268,11071040）;福州大学科技发展基金资助项目（2011-xq.22） |
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| 摘 要： | 首先给出了加法范畴的Abel化与幂等完备化的关系，证明了加法范畴的幂等完备化范畴是其Abel化范畴的投射子范畴；在此基础上，证明了三角范畴recollement的Abel化是Abel范畴的右recollement。
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| 关 键 词： | 三角范畴 Abel化 recollement |
Recollement and Abelian of Triangulated Category |
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| TANG Li-dan,CHEN Qing-hua.Recollement and Abelian of Triangulated Category[J].Journal of Putian College,2012(5):1-4,13. |
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| Authors: | TANG Li-dan CHEN Qing-hua |
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| Institution: | 1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou Fujian 350108, China; 2. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou Fujian 350007, China ) |
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| Abstract: | The relationship between Abelian and idempotent completion of additive categories was presented in this paper. It proves that the idempotent completion of an additive category is the subcategory of its Abelian category, which consists of all the projectives. Then we prove that the Abelian of a recollement of triangulated categories is a right recollement of Abelian categories. |
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| Keywords: | triangulated category Abelian recollement |
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