Adhesivity with partial maps instead of spans
This paper is a journal version of a conference paper [Lect. Notes Comput. Sci. 6372, 250--265 (2010; Zbl 1306.68073)] presented at ICGT 2010. The main idea is to propose a new categorical framework for graph transformation and high-level replacement (HLR) systems, which generalizes adhesive categories and several variants introduced recently in the literature. The author proposes ``partial map adhesive categories'' based on ''heraditary pushouts''as a natural candidate for such a framework. In fact, several interesting properties are shown for this framework, which are fundamental for the theory of HLR systems including different kinds of graph and Petri net transformation systems. Moreover, partial map adhesivity can be shown via partial map classifiers leading to an interesting proof technique. Partial map adhesive categories are shown to be strictly more general than weak adhesive HLR categories. On the other hand partial map adhesive are also ``vertical'' weak adhesive HLR categories, but the equivalence of both is (stated as) an open problem. In contrast to the present paper vertical weak adhesive HLR categories are proposed in [the reviewer, \textit{U. Golas} and \textit{F. Hermann}, Bull. Eur. Assoc. Theor. Comput. Sci. EATCS 102, 111--121 (2010; Zbl 1257.68092)] as a natural candidate for a general rewriting framework. In any case both approaches are very powerful and can benefit from each other.
scientific article; zbMATH DE number 6054481