“…Overall, and as discussed throughout the paper, but in particular in full detail in Section 4, our approach to determining suitable classes of categories supporting the various rewriting semantics relies heavily on the categorical rewriting and category theory literature, such as the traditional framework of Ehrig et al that is based upon the notion of M-adhesive categories [3], but also a large number of works on a variety of other categories with adhesivity properties [5,4,40,38,41,6,35,36,20,7]. As discussed in further detail in Example 2 and in Section 5, there exist practically relevant application examples of rewriting theories that require to generalize the categorical formalism even further, e.g., to (M,N)-adhesive categories [42,43], of which in particular the category SGraph of directed simple graphs was recently found [44] to provide a non-trivial example (cf. the discussion in Example 2 for further details).…”