Dialectical nets: A categorical approach to net theory

A new approach to the modelling of net theory with tools from category theory called dialectical nets is reviewed. The main idea involves the use of the theory of generalized metric spaces to model the structure of a net. 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. The production and use of the net are modelled as an adjunct pair of functions. These functions are constructed from the generalized relations between the places and the transitions.