The constraint satisfaction problem (CSP) is a computational problem that includes a range of important problems in computer science. We point out that fundamental concepts of the CSP, such as the solution set of an instance and polymorphisms, can be formulated abstractly inside the 2-category $\mathcal{P}\mathbf{FinSet}$ of finite sets and sets of functions between them. The 2-category $\mathcal{P}\mathbf{FinSet}$ is a quantaloid, and the formulation relies mainly on structure available in any quantaloid. This observation suggests a formal development of generalisations of the CSP and concomitant notions of polymorphism in a large class of quantaloids. We extract a class of optimisation problems as a special case, and show that their computational complexity can be classified by the associated notion of polymorphism.

翻译：限制满意度问题(CSP)是一个计算问题,其中包括计算机科学的一系列重要问题。我们指出,CSP的基本概念,如实例和多形态的解决方案集等,可以抽象地在限量组和功能组的2类内抽象地形成。2类的$mathcal{P ⁇ mathbf{FinSet} 是一个孔,其配方主要依赖任何孔形的结构。这一观察表明,CSP的概括性以及随之而来的大型类孔形体多形态概念正在正式形成。我们将优化问题分类作为特例,并表明其计算复杂性可以按相关的多形态概念分类。