License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2023.6
URN: urn:nbn:de:0030-drops-188032
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Turkenburg, Ruben ; Beohar, Harsh ; Kupke, Clemens ; Rot, Jurriaan

Forward and Backward Steps in a Fibration

LIPIcs-CALCO-2023-6.pdf (0.7 MB)


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.

BibTeX - Entry

  author =	{Turkenburg, Ruben and Beohar, Harsh and Kupke, Clemens and Rot, Jurriaan},
  title =	{{Forward and Backward Steps in a Fibration}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-287-7},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{270},
  editor =	{Baldan, Paolo and de Paiva, Valeria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-188032},
  doi =		{10.4230/LIPIcs.CALCO.2023.6},
  annote =	{Keywords: Coalgebra, Fibration, Bisimilarity}

Keywords: Coalgebra, Fibration, Bisimilarity
Collection: 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)
Issue Date: 2023
Date of publication: 02.09.2023

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