Tilting Theory and Functor Categories I. Classical Tilting
نویسندگان
چکیده
منابع مشابه
Derived Categories and Tilting
We review the basic definitions of derived categories and derived functors. We illustrate them on simple but non trivial examples. Then we explain Happel’s theorem which states that each tilting triple yields an equivalence between derived categories. We establish its link with Rickard’s theorem which characterizes derived equivalent algebras. We then examine invariants under derived equivalenc...
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TILTING THEORY FOR QUIVERS AND RELATED CATEGORIES MORITZ GROTH AND JAN ŠŤOVÍČEK Abstract. We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between the corresponding representation theories with values in arbitrary s...
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Tilting theory provides a good method for comparing two categories, such as module categories of finite-dimensional algebras. For an introduction, see e.g. [A]. BGP reflection functors [BGP] give a way of comparing the representation categories of two quivers, where one is obtained from the other by reversing all of the arrows incident with a sink or source. Auslander, Platzeck and Reiten [APR]...
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ژورنال
عنوان ژورنال: Applied Categorical Structures
سال: 2013
ISSN: 0927-2852,1572-9095
DOI: 10.1007/s10485-013-9322-y