# ω-Ind Completion of Monoidal Categories and Infinite Petri Net Computations.

Meseguer, J., Montanari, U. and Sassone, V. (1993) ω-Ind Completion of Monoidal Categories and Infinite Petri Net Computations. In, Workshop on Topology and Completion in Semantics, Chartres, France, , 51 pp..

## Description/Abstract

There exists a KZ-doctrine on the 2-category of the locally small categories whose algebras are exactly the categories which admits all the colimits indexed by $\omega$-chains. The paper presents a wide survey of this topic. In addition, we show that this chain cocompletion KZ-doctrine lifts smoothly to KZ-doctrines on (many variations of) the 2-categories of monoidal and symmetric monoidal categories, thus yielding a universal construction of colimits of $\omega$-chains in those categories. Since the processes of Petri nets may be axiomatized in terms of symmetric monoidal categories this result provides a universal construction of the algebra of infinite processes of a Petri net.

Item Type: Conference or Workshop Item (Paper) Event Dates: 1993 petri nets semantics, infinite computations, symmetric monoidal categories, omega inductive completion of categories Faculty of Physical Sciences and Engineering > Electronics and Computer Science > Web & Internet Science 261872 28 Jan 2006 27 Mar 2014 20:04 Google Scholar http://eprints.soton.ac.uk/id/eprint/261872