基于稳定同伦理论的树的倾斜理论
Tilting theory for trees via stable homotopy theory
摘要：
我们表明，变种的经典反射函子从ESTA表示论存在于任何抽象的稳定同伦理论，使他们可用，例如在任意的地面环，拟相干模的计划，在微分分次上下文中，在稳定的同伦理论以及在等变，motivic，和参数化的变体。作为这些等价的应用，我们获得了在所有这些情况下有效的树的抽象倾斜结果，从而推广了Happel的结果。这些反射函子的主要工具介绍的建设同伦满态的小范畴和一点扩张的小范畴，这两个启发类似的概念，在同调代数。
英文摘要：
We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasi-coherent modules on schemes, in the differential-graded context, in stable homotopy theory as well as in the equivariant, motivic, and parametrized variant thereof. As an application of these equivalences we obtain abstract tilting results for trees valid in all these situations, hence generalizing a result of Happel. The main tools introduced for the construction of these reflection functors are homotopical epimorphisms of small categories and one-point extensions of small categories, both of which are inspired by similar concepts in homological algebra.
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