Amalgamating Pushout and Pullback Graph Transformation in Collagories

The relation-algebraic approach to graph transformation replaces the universal category-theoretic characterisations of pushout and pullbacks with the local characterisations of tabulations and co-tabulations. The theory of collagories is a weak axiomatisation of relation-algebraic operations that closely corresponds to adhesive categories.We show how to amalgamate double-pushout and double-pullback rewriting steps into a fused rewriting concept where rules can contain subgraph variables in a natural and flexible way, and rewriting can delete or duplicate the matched instances of such variables.