| 关于Abelian三角范畴的一个注记 |
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| 引用本文： | 许萍虹,辛林.关于Abelian三角范畴的一个注记[J].福建师范大学学报(自然科学版),2009,25(6). |
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| 作者姓名： | 许萍虹 辛林 |
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| 作者单位： | 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 |
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| 摘 要： | 主要证明如下结论:如果(C,T,Δ)是三角范畴,则C是Abelian范畴的充分且必要条件是C中三角是由同构于如下形式的态射图构成:U⊕V(00/01)→W⊕V(00/10)→T(U)⊕W(10/00)T(U)⊕T(V).由此得到:如果C是一个Abelian范畴,T是C上的可逆加法自函子,则有且仅有一种方式使(C,T)构成三角范畴.另外,还通过Abelian范畴C上的Serre类,研究局部化范畴CS-1]是Abelian三角范畴的条件.
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| 关 键 词： | 三角范畴 阿贝尔范畴 范畴局部化 半单范畴 |
A Note on an Abelian Triangulated Category |
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| XU Ping-hong,XIN Lin.A Note on an Abelian Triangulated Category[J].Journal of Fujian Teachers University(Natural Science),2009,25(6). |
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| Authors: | XU Ping-hong XIN Lin |
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| Institution: | XU Ping-hong,XIN Lin(School of Mathematics and Computer Science,Fujian Normal University,Fuzhou 350007,China) |
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| Abstract: | Show that if ((E), T, A) is a triangulated category, then (E) is an Abelian category if and only if the collection of diagramsXu→Yv→Zw→T(X) in (E) which are isomorphic to the diagrams of the form U⊕V(_0 1~0 0)→W⊕V(_1 0~0 0)→T(U)⊕W(_0 0~1 0)→T(U)⊕T(V)are triangulations. So if (E) is an Abelian category and T is an additive functor which is an automorphism of the category (E). Then have only a way to make ((E),T) a triangulated category. Moreover also inverstigate the conditions for the localization (E) S~(-1)] to be an Abelian triangulated category via a Serre class on the Abelian category (E). |
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| Keywords: | triangulated category Abelian category localization of category semisimple category |
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