Allegories and Collagories for Transformation of Graph Structures Considered as Coalgebras

Although coalgebras are widely used to model dynamic systems with infinite behaviours, they are actually also a more natural tool than algebras to model the static systems that are the main subject of the “algebraic approach” to graph transformation and model transformation: many variants of graph structures and object webs are more easily modelled as coalgebras than as algebras. By characterising the kinds of coalgebras that give rise to different kinds of allegories, we make the tools of the relation-algebraic approach and also of the category-theoretic “adhesive” “algebraic approach” available to the transformations of coalgebras.