From triangulated categories to module categories via localisation II: calculus of fractions
From triangulated categories to module categories via localisation II: calculus of fractions
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DOI：
10.1112/jlms/jdt015
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发表时间：
2013-04
期刊：
影响因子：
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通讯作者：
A. B. Buan;Robert J. Marsh
中科院分区：
文献类型：
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作者：
A. B. Buan;Robert J. Marsh
我们证明了一个Hom有限的三角化范畴C与函子HomC（T，−）的核的商是Preabel的，其中T是刚性对象.我们进一步表明，一类正规态射的商承认一个演算的左，右分数。由此可见，在正则态射类上的商的Gabriel-Zisman局部化是阿贝尔的。证明了它等价于C中T的自同态代数上的有限维模范畴。
We show that the quotient of a Hom-finite triangulated category C by the kernel of the functor HomC(T, −), where T is a rigid object, is preabelian. We further show that the class of regular morphisms in the quotient admit a calculus of left and right fractions. It follows that the Gabriel-Zisman localisation of the quotient at the class of regular morphisms is abelian. We show that it is equivalent to the category of finite dimensional modules over the endomorphism algebra of T in C.