Adhesive categories provide an abstract framework for the algebraic approach to rewriting theory, where many general results can be recast and uniformly proved. However, checking that a model satisfies the adhesivity properties is sometimes far from immediate. In this paper we present a new criterion giving a sufficient condition for $\mathcal{M}, \mathcal{N}$-adhesivity, a generalisation of the original notion of adhesivity. We apply it to several existing categories, and in particular to hierarchical graphs, a formalism that is notoriously difficult to fit in the mould of algebraic approaches to rewriting and for which various alternative definitions float around.
翻译:Adhesive 类别为重写理论的代数法提供了一个抽象框架,许多一般结果可以重新编写并统一证明。 但是,有时很难立即检查一个符合粘合性特性的模型。 在本文件中,我们提出了一个新标准,为$\mathcal{M},\ mathcal{N}$-adhesitical提供了充分的条件,概括了原有的粘合性概念。我们将其应用于几个现有类别,特别是等级图,这是一种形式主义,很难适应重写代数法的模版,而且各种替代定义都存在。