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
1993
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
.
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Conference or Workshop Item
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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
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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: 10 Sep 2024 01:40
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Contributors
Author:
J. Meseguer
Author:
U. Montanari
Author:
V. Sassone
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