MSO transductions are binary relations between structures which are defined using monadic second-order logic. MSO transductions form a category, since they are closed under composition. We show that many notions from language theory, such as recognizability or tree decompositions, can be defined in an abstract way that only refers to MSO transductions and their compositions.

翻译：MSO 转导是结构之间使用一元二阶逻辑定义的二元关系。MSO 转导在复合运算下封闭，因此构成一个范畴。我们证明，语言理论中的许多概念，如可识别性或树分解，都可以通过仅涉及 MSO 转导及其复合的抽象方式加以定义。