Locating Reactions using 2-Categories
Locating Reactions using 2-Categories
Groupoidal relative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner's approach to deriving labelled bisimulation congruences from reduction systems. In this paper, we develop the theory of GRPOs further, proving that well-known equivalences, other than bisimulation, are congruences. To demonstrate the type of category theoretic arguments which are inherent in the 2-categorical approach, we construct GRPOs in a category of 'bunches and wirings.' Finally, we prove that the 2-categorical theory of GRPOs is a generalisation of the approaches based on Milner's precategories and Leifer's functorial reactive systems.
bisimulation congruences, reduction systems, transition systems, coinduction principles, bigraphs, bunches, 2-categories, bicategories
297-327
Sassone, V.
df7d3c83-2aa0-4571-be94-9473b07b03e7
Sobocinski, P.
439334ab-2826-447b-9fe5-3928be3fd4fd
2005
Sassone, V.
df7d3c83-2aa0-4571-be94-9473b07b03e7
Sobocinski, P.
439334ab-2826-447b-9fe5-3928be3fd4fd
Sassone, V. and Sobocinski, P.
(2005)
Locating Reactions using 2-Categories.
Theoretical Computer Science, 333 (1-2), .
Abstract
Groupoidal relative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner's approach to deriving labelled bisimulation congruences from reduction systems. In this paper, we develop the theory of GRPOs further, proving that well-known equivalences, other than bisimulation, are congruences. To demonstrate the type of category theoretic arguments which are inherent in the 2-categorical approach, we construct GRPOs in a category of 'bunches and wirings.' Finally, we prove that the 2-categorical theory of GRPOs is a generalisation of the approaches based on Milner's precategories and Leifer's functorial reactive systems.
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Published date: 2005
Keywords:
bisimulation congruences, reduction systems, transition systems, coinduction principles, bigraphs, bunches, 2-categories, bicategories
Organisations:
Web & Internet Science, Electronic & Software Systems
Identifiers
Local EPrints ID: 261842
URI: http://eprints.soton.ac.uk/id/eprint/261842
ISSN: 0304-3975
PURE UUID: 5ca4cf73-12f3-4cc6-99e7-f06e3b0aea01
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Date deposited: 27 Jan 2006
Last modified: 14 Mar 2024 07:00
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Contributors
Author:
V. Sassone
Author:
P. Sobocinski
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