标题： 抽象稳定同伦理论的特征 显示英文标题

标题： Characterizations of abstract stable homotopy theories

摘要： 在本文中，我们建立了稳定导出器的新特征，从而得到了从（指向的）拓扑空间到谱以及更一般地到稳定化的传递的额外解释。 我们证明，当且仅当同伦有限极限和同伦有限余极限交换时，导出器是稳定的，并且对于足够有限的Kan扩张有相应的变体。 作为另一种重新表述，当且仅当导出器包含零对象，并且在平方上部分锥形和部分纤维态射交换时，导出器是稳定的。 显示英文摘要

摘要： In this paper we establish new characterizations of stable derivators, thereby obtaining additional interpretations of the passage from (pointed) topological spaces to spectra and, more generally, of the stabilization. We show that a derivator is stable if and only if homotopy finite limits and homotopy finite colimits commute, and there are variants for sufficiently finite Kan extensions. As an additional reformulation, a derivator is stable if and only if it admits a zero object and if partial cone and partial fiber morphisms commute on squares.