A new criterion for $\mathcal{M}, \mathcal{N}$-adhesivity, with an application to hierarchical graphs

TL;DR

This paper introduces a new criterion for $\

Contribution

It provides a sufficient condition for $\

Findings

Applied to hierarchical graphs, the criterion simplifies verifying adhesivity.

Extended the class of categories known to be $\

demonstrated the criterion's effectiveness on several existing categories.

Abstract

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.