$\mathcal{M}, \mathcal{N}$ -粘附性的新判据及其在层次图中的应用
A new criterion for $\mathcal{M}, \mathcal{N}$-adhesivity, with an application to hierarchical graphs
摘要：
粘着范畴为重写理论的代数方法提供了一个抽象的框架，其中许多一般性的结果可以被改写和统一证明。然而，检查模型是否满足粘附性属性有时远非立即。在本文中，我们提出了一个新的标准给出了一个充分条件$\mathcal{M}, \mathcal{N}$ -adhesivity，原来的概念的adhesivity的推广。我们将其应用到几个现有的类别，特别是层次图，一种形式主义，是出了名的难以适应的模具代数方法重写和各种替代的定义浮动。
英文摘要：
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.
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