In this paper, we investigate the relationship between two elementary operations on derivations in the framework of graph transformation based on adhesive categories: moving a derivation along a derivation based on parallel and sequential independence on one hand and restriction of a derivation with respect to a monomorphism into the start object on the other hand. Intuitively, a restriction clips off parts of the start object that are never matched by a rule application throughout the derivation on the other hand. As main result, it is shown that moving a derivation preserves its spine being the minimal restriction.

@article{paperbot3427,
  title = {Moving a Derivation Along a Derivation Preserves the Spine in Adhesive Categories},
  author = {Hans-Jörg Kreowski and Aaron Lye and Aljoscha Windhorst},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 21, Issue 2},
  year = {2025},
  doi = {10.46298/lmcs-21(2:4)2025}
}