Rewriting on cyclic structures

We present a categorical formulation of the rewriting of possibly cyclic term graphs, and the proof that this presentation is equivalent to the well-accepted operational definition proposed by Barendregt et al., but for the case of circular redexes, for which we propose (and justify formally) a different treatment. The categorical framework, based on suitable 2-categories, allows to model also automatic garbage collection and rules for sharing/unsharing and folding/unfolding of structures. Furthermore, it can be used for defining various extensions of term graph rewriting, and for relating it to other rewriting formalisms.