2010): Categorical Frameworks for Graph Transformation and

Several variants of high-level replacement (HLR) and adhesive cate-gories have been introduced in the literature as categorical frameworks for graph transformation and HLR systems based on the double pushout (DPO) approach. In addition to HLR, adhesive, and adhesive HLR categories sev-eral weak variants, especially weak adhesive HLR with horizontal and ver-tical variants, as well as partial variants, including partial map adhesive and partial VK square adhesive categories are reviewed and related to each other. We propose as weakest version the class of vertical weak adhesive HLR cate-gories, shortM-adhesive categories, which are still sufficient to obtain most of the main results for graph transformation and HLR systems. The results in this paper are summarized in Fig. 1 showing a hierarchy of all these vari-ants of adhesive, adhesive HLR, andM-adhesive categories, which can be considered as different categorical frameworks for graph transformation and HLR systems