Turkenburg, R., Beohar, H. orcid.org/0000-0001-5256-1334, Kupke, C. et al. (1 more author) (2023) Forward and backward steps in a fibration. In: Baldan, P. and de Paiva, V., (eds.) 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023), 19-21 Jun 2023, Padova, Italy. Leibniz International Proceedings in Informatics (LIPIcs), 270 . Schloss Dagstuhl – Leibniz-Zentrum für Informatik , 6:1-6:18.
Abstract
Distributive laws of various kinds occur widely in the theory of coalgebra, for instance to model automata constructions and trace semantics, and to interpret coalgebraic modal logic. We study steps, which are a general type of distributive law, that allow one to map coalgebras along an adjunction. In this paper, we address the question of what such mappings do to well known notions of equivalence, e.g., bisimilarity, behavioural equivalence, and logical equivalence. We do this using the characterisation of such notions of equivalence as (co)inductive predicates in a fibration. Our main contribution is the identification of conditions on the interaction between the steps and liftings, which guarantees preservation of fixed points by the mapping of coalgebras along the adjunction. We apply these conditions in the context of lax liftings proposed by Bonchi, Silva, Sokolova (2021), and generalise their result on preservation of bisimilarity in the construction of a belief state transformer. Further, we relate our results to properties of coalgebraic modal logics including expressivity and completeness.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © Ruben Turkenburg, Harsh Beohar, Clemens Kupke, and Jurriaan Rot; licensed under Creative Commons License CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/) |
Keywords: | Coalgebra; Fibration; Bisimilarity |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 21 Jun 2024 11:58 |
Last Modified: | 21 Jun 2024 12:32 |
Status: | Published |
Publisher: | Schloss Dagstuhl – Leibniz-Zentrum für Informatik |
Series Name: | Leibniz International Proceedings in Informatics (LIPIcs) |
Refereed: | Yes |
Identification Number: | 10.4230/LIPIcs.CALCO.2023.6 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:213739 |