ABSTRACT
Courser's paper views dynamic networks as representatives of a "decorated cospan category", or labelled directed graph with inputs, outputs and weighted edges all specified by the pertinent cospans. Graph-theoretic research includes Koch et al.'s work on formalizing opetopes using a combination of nested rings and trees. Courser shows that when a category with pullbacks has finite limits, decorated cospans are morphisms in a symmetric monoidal bicategory, while maps of spans are 2-morphisms. Eugene Lerman and David Spivak have chosen to work with operads in a 2-category setting, to characterize maps between dynamical systems that are, in turn, viewed as maps in the 2-category. Relational ologs are based on Rel, the category of sets and relations. Stell's more general approach to Formal Concept Analysis, involving application of techniques derived from mathematical morphology to hypergraphs, also helps to link semantic technology to these more narrowly-construed ontological initiatives.
