Abstract tilting theory for quivers and related categories
Abstract tilting theory for quivers and related categories
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箭袋及相关类别的抽象倾斜理论
DOI：
10.2140/akt.2018.3.71
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
J. Šťovíček
中科院分区：
文献类型：
--
作者：
Moritz Groth;J. Šťovíček
我们将经典颤振表示理论中的反射函子构造推广到具有自由附加汇或源的任意小范畴。这些反射模态可以在相应的表示理论与任意稳定同伦理论中的值之间产生等价，包括域上的表示、环上的表示或方案上的表示以及微分梯度表示和谱表示。
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 stable homotopy theories, including representations over fields, rings or schemes as well as differential-graded and spectral representations.
Specializing to representations over a field and to specific shapes, this recovers derived equivalences of Happel for finite, acyclic quivers. However, even over a field our main result leads to new derived equivalences for example for not necessarily finite or acyclic quivers.
The results obtained here rely on a careful analysis of the compatibility of gluing constructions for small categories with homotopy Kan extensions and homotopical epimorphisms, as well as on a study of the combinatorics of amalgamations of categories.
通过稳定同伦理论的树木倾斜理论
影响因子：
0.8
作者：
Moritz with Stovicek
通讯作者：
Moritz with Stovicek
幺半群导数中痕量的可加性
DOI：
10.1017/is014005011jkt262
发表时间：
2014
期刊：
arXiv: Algebraic Topology
影响因子：
--
作者：
Moritz with Ponto;Shulman
通讯作者：
Shulman