Changing Labels in the Double-Pushout Approach Can Be Treated Categorically

In the double-pushout approach to graph transformations, most authors assume the left-hand side to be injective, since the noninjective case leads to ambiguous results. Taking into consideration productions that change labels, however, may add ambiguity even in the case of injective graph productions. A well-known solution to this problem is restricting the categorical treatment to the underlying graphs, whereas the labels on the derived graph are defined by other means. In this paper, we resume the detailed results on arbitrary left-hand sides that Ehrig and Kreowski have already given in 1976. We apply these results to the case of relabeling such that we can retain the elegant categorical constructions at the level of labeled graphs.