| 关于三角范畴的八面体公理 |
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| 引用本文： | 许庆兵,王正萍,张孔生.关于三角范畴的八面体公理[J].数学研究,2013(1):91-99. |
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| 作者姓名： | 许庆兵 王正萍 张孔生 |
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| 作者单位： | 滁州职业技术学院;东南大学数学系 |
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| 基金项目： | 安徽省高校省级自然科学基金(KJ20122300,KJ2011B119) |
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| 摘 要： | 三角范畴是一个带有自同构且满足四条公理的加法范畴,其中的一条重要公理就是八面体公理,该公理形式复杂不易理解难以应用.在本文中,作者讨论了三角范畴定义中八面体公理的几个等价命题,给出了新的八面体公理的等价命题,证明了各个公理间的相互等价关系,同时简化了八面体的表达形式,并且给出了该定理的一个具体应用.
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| 关 键 词： | 三角范畴 八面体公理 同伦Cartesian |
On the Octahedral Axiom of Triangulated Categories |
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| Xu Qingbing,Wang Zhengping,Zhang Kongsheng.On the Octahedral Axiom of Triangulated Categories[J].Journal of Mathematical Study,2013(1):91-99. |
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| Authors: | Xu Qingbing Wang Zhengping Zhang Kongsheng |
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| Affiliation: | 1.The Vocational and Technical College of Chuzhou,Chuzhou Anhui 239000; 2.Department of Mathematics Southeast university,Nanjing Jiangsu 210096) |
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| Abstract: | A triangulated category is an additive category with an automorphism, it satisfies four axioms. One of which is called the octahedral axiom and plays an important role in representation Theory. The form of the octahedral axiom is too complex and difficult to apply, it is often misunderstood and considered irrelevant. In this paper, several equivalent propositions of the octahedral axiom of triangulated category are studied, the simplified form of the octahedral axiom and its concrete application are given. |
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| Keywords: | Triangulated categories The octahedral axiom Homotopy cartesian |
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