We give analogues of the Auslander correspondence for two classes of triangulated categories satisfying certain finiteness conditions. The first class is triangulated categories with additive generators and we consider their endomorphism algebras as the Auslander algebras. For the second one, we introduce the notion of $[1]$-additive generators and consider their graded endormorphism algebras as the Auslander algebras. We give a homological characterization of the Auslander algebras for each class. Along the way, we also show that the algebraic triangle structures on the homotopy categories are unique up to equivalence.

中文翻译：

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三角化类别的 Auslander 对应关系

我们给出了满足某些有限条件的两类三角化范畴的 Auslander 对应的类比。第一类是具有加法生成器的三角剖分类别，我们将它们的自同态代数视为 Auslander 代数。对于第二个，我们引入了 $[1]$-additive generators 的概念，并将它们的分级内同态代数视为 Auslander 代数。我们给出了每个类的 Auslander 代数的同调表征。在此过程中，我们还证明了同伦范畴上的代数三角形结构在等价之前是唯一的。