Series B: Technical Reports, No. 8. Espoo, Finland: Helsinki Unversity of Technology, Digital Systems Laboratory, November 1989.
Abstract: A new approach to the modelling of net theory with the tools from category theory called dialectical nets is reviewed. The main idea involves the use of the theory of generalized metric spaces. The arcs in a net are viewed as generalized relations between places and transitions. The category theoretical notion of adjunction is used to model the dialectical notion of opposing tendencies. Thus for a net the production and consumption in the net are modelled as an adjoint pair of functors. These functors are constructed from the generalized relations between places and transitions.
Keywords: dialectical net; categorial approach (to net theory); generalized metric space; adjoint functor; opposing tendency.