Kind Bigraphs

We present a refinement, suggested by Jensen and Milner under the term kind, of pure bigraphs. We name the result kind bigraphs. This refinement generalises the notion of atomic and non-atomic controls, allowing a control to contain a subset of the set of controls.We show that this variation has relative pushouts and classify its idem pushouts. A canonical labelled transition system can be derived from this classification and we use known results to reason about bisimilarity on this transition system. We show how kind bigraphs can be used to describe Milner's homomorphic sortings and finally discuss the extra expressivity that parametric kind reaction rules allow.