We give a general notion of combinatory completeness with respect to a faithful cartesian club and use it systematically to obtain characterisations of a number of different kinds of applicative system. Each faithful cartesian club determines a notion of structured multicategory, with the different notions of structured multicategory obtained in this way giving different notions of polynomial over an applicative system, which in turn give different notions of combinatory completeness. We obtain the classical characterisation of combinatory algebras as combinatory complete applicative systems as a specific instance.

翻译：我们提出了相对于忠实笛卡尔簇的组合完备性的一般概念，并系统地利用它来刻画多种不同类型的应用系统。每个忠实笛卡尔簇确定了一类结构化多重范畴的概念，通过这种方式获得的不同结构化多重范畴概念又给出了应用系统上多项式的不同定义，进而导出了组合完备性的不同概念。我们将组合代数刻画为组合完备应用系统的经典结论作为本文框架的一个具体实例。