In this paper we continue the project of generalizing tilting theory to the category of contravariant functors Mod(C), from a skeletally small preadditive category C to the category of abelian groups, initiated in [15]. We introduce the notion of a generalized tilting category T, and we concentrate here on extending Happel's theorem to Mod(C); more specifically, we prove that there is an equivalence of triangulated categories D~b(Mod(C)) D ~b(Mod(T)). We then add some restrictions on our category C, in order to obtain a version of Happel's theorem for the categories of finitely presented functors. We end the paper proving that some of the theorems for artin algebras, relating tilting with contravariantly finite categories proved in Auslander and Reiten (Adv Math 12(3):306-366, 1974; Adv Math 86(1):111-151, 1991), can be extended to the category of finitely presented functors Mod(C), with C a dualizing variety.
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机译：在本文中，我们继续将倾斜理论推广到逆变函子Mod（C）类别的项目，从骨架较小的前加性类别C到阿贝尔群的类别，始于[15]。我们介绍了广义倾斜类别T的概念，在这里我们集中于将Happel定理扩展到Mod（C）。更具体地说，我们证明了三角类D〜b（Mod（C））D〜b（Mod（T））的等价性。然后，我们对类别C添加一些限制，以便获得有限表示函子类别的Happel定理的一个版本。我们结束本文的工作，证明了关于artin代数的一些定理，在Auslander和Reiten中证明了与倾斜与有限有限类别相关的（Adv Math 12（3）：306-366，1974; Adv Math 86（1）：111-151， 1991），可以扩展到有限表示函子Mod（C）的类别，其中C是对偶函数。
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