Process models of graph transformation systems are based on the concept of occurrence grammars, which are a generalization of Petri net processes given by occurrence nets. Recently, subobject transformation systems were proposed as an abstract framework for occurrence grammars in adhesive categories, but they are restricted to monomorphic matches for transformation steps. In this paper we review the construction of STSs as processes for plain graph grammars and present an extension to weak adhesive HLR categories with non-monomorphic matching, such that e.g. attributed graph grammars are included
