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ω-Inductive completion of monoidal categories and infinite petri net computations

ω-Inductive completion of monoidal categories and infinite petri net computations
ω-Inductive completion of monoidal categories and infinite petri net computations
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 ω-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 ω-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.
petri nets semantics, infinite computations, symmetric monoidal categories, omega inductive completion of categories
Meseguer, J.
fdb4acf3-5cf5-440b-8618-8aeb9d0159d1
Montanari, U.
45418952-b856-4910-94c1-5ff3c7c19938
Sassone, V.
df7d3c83-2aa0-4571-be94-9473b07b03e7
Meseguer, J.
fdb4acf3-5cf5-440b-8618-8aeb9d0159d1
Montanari, U.
45418952-b856-4910-94c1-5ff3c7c19938
Sassone, V.
df7d3c83-2aa0-4571-be94-9473b07b03e7

Meseguer, J., Montanari, U. and Sassone, V. (1993) ω-Inductive completion of monoidal categories and infinite petri net computations. Workshop on Topology and Completion in Semantics, Chartres, France. 51 pp .

Record type: Conference or Workshop Item (Paper)

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 ω-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 ω-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.

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Published date: 1993
Additional Information: Event Dates: 1993
Venue - Dates: Workshop on Topology and Completion in Semantics, Chartres, France, 1993-01-01
Keywords: petri nets semantics, infinite computations, symmetric monoidal categories, omega inductive completion of categories
Organisations: Web & Internet Science

Identifiers

Local EPrints ID: 261872
URI: http://eprints.soton.ac.uk/id/eprint/261872
PURE UUID: 745205e0-a2c4-4e9b-8ba1-3742d5cf3b2a

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Date deposited: 28 Jan 2006
Last modified: 14 Mar 2024 07:00

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Contributors

Author: J. Meseguer
Author: U. Montanari
Author: V. Sassone

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