We present a study of the notion of coalgebraic simulation introduced by Hughes and Jacobs. Although in their original paper they allow any functorial order in their definition of coalgebraic simulation, for the simulation relations to have good properties they focus their attention on functors with orders which are strongly stable. This guarantees a so-called "composition-preserving" property from which all the desired good properties follow. We have noticed that the notion of strong stability not only ensures such good properties but also "distinguishes the direction" of the simulation. For example, the classic notion of simulation for labeled transition systems, the relation "p is simulated by q", can be defined as a coalgebraic simulation relation by means of a strongly stable order, whereas the opposite relation, "p simulates q", cannot. Our study was motivated by some interesting classes of simulations that illustrate the application of these results: covariant-contravariant simulations and conformance simulations.

翻译：本文研究了由Hughes和Jacobs引入的余代数模拟概念。尽管他们在原始论文中允许在余代数模拟定义中使用任意函子序，但为使模拟关系具有良好性质，他们将注意力集中在具有强稳定序的函子上。这确保了所谓的"保复合性"，由此可推导出所有期望的良好性质。我们发现强稳定性概念不仅保证了这些良好性质，还"区分了模拟的方向"。例如，对于标记转移系统的经典模拟概念，关系"p被q模拟"可以通过强稳定序定义为余代数模拟关系，而相反关系"p模拟q"则不能。我们的研究源于几类有趣的模拟应用实例：协变-逆变模拟和一致性模拟。