Tilting theory has been a very important tool in the classification of finite dimensional algebras of finite and tame representation type, as well as, in many other branches of mathematics. Happel (1988) and Cline et al. (J Algebra 304:397-409 1986) proved that generalized tilting induces derived equivalences between module categories, and tilting complexes were used by Rickard (J Lond Math Soc 39:436- 456, 1989) to develop a general Morita theory of derived categories. On the other hand, functor categories were introduced in representation theory by Auslander (I Commun Algebra 1(3):177-268, 1974), Auslander (1971) and used in his proof of the first Brauer-Thrall conjecture (Auslander 1978) and later on, used systematically in his joint work with I. Reiten on stable equivalence (Auslander and Reiten, Adv Math 12(3):306-366, 1974), Auslander and Reiten (1973) and many other applications. Recently, functor categories were used in Martínez-Villa and Solberg (J Algebra 323(5):1369-1407, 2010) to study the Auslander-Reiten components of finite dimensional algebras. The aim of this paper is to extend tilting theory to arbitrary functor categories, having in mind applications to the functor category Mod(mod_Λ), with Λ a finite dimensional algebra.
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机译：倾斜理论一直是有限和驯服表示类型的有限维代数分类以及其他许多数学分支中非常重要的工具。 Happel（1988）和Cline等。 （J Algebra 304：397-409 1986）证明广义倾斜引起模块类别之间的导出等价物，并且Rickard使用倾斜复合体（J Lond Math Soc 39：436-456，1989）来发展一般Morita派生类别理论。另一方面，函子类别由Auslander（I Commun Algebra 1（3）：177-268，1974），Auslander（1971）在表示理论中引入，并用于他对第一个Brauer-Thrall猜想的证明（Auslander 1978）。后来，在与I. Reiten的联合等效研究中被系统地使用（Auslander和Reiten，Adv Math 12（3）：306-366，1974），Auslander和Reiten（1973）和许多其他应用。近年来，在Martínez-Villa和Solberg中使用函子类别（J Algebra 323（5）：1369-1407，2010）来研究有限维代数的Auslander-Reiten分量。本文的目的是将倾斜理论扩展到任意函子类别，并牢记应用到具有有限维代数的函子类别Mod（mod_Λ）。
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