Hypergraph rewriting using conformisms

Abstract In this paper we study single-pushout transformation in a category of spans, a generalization of the notion of partial morphism in, for instance, [2,4]. As an application, single-pushout transformation in a category of hypergraphs with a special type of partial morphisms, the conformisms, is presented. In particular, we show the existence of the pushout of any pair of conformisms of hypergraphs with the same source hypergraph, and how to construct one such a pushout. Finally, hypergraph rewriting using conformisms is compared to single-pushout hypergraph rewriting by means of a detailed example.