A note on outward and inward productions in the categorical graph-grammar approach and Delta-grammars

By proving the correspondence between the usual double-pushout approach and Banach’s inward version in a purely categorical setting, we can extend the latter to noninjective left-hand sides. In the injective case, Banach’s point of view establishes a close relationship between the categorical approach and Kaplan’s ∆-grammars allowing a slight generalization of ∆-grammars and making them an operational description of the categorical approach.