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Aczel-Mendler Bisimulations in a Regular Category

Author Jérémy Dubut

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Jérémy Dubut
  • National Institute of Advanced Science and Technology, Tokyo, Japan

Funding

The author is supported by JST, CREST Grant Number JPMJCR22M1, Japan.

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Jérémy Dubut. Aczel-Mendler Bisimulations in a Regular Category. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.CALCO.2023.19

Abstract

Aczel-Mendler bisimulations are a coalgebraic extension of a variety of computational relations between systems. It is usual to assume that the underlying category satisfies some form of axiom of choice, so that the theory enjoys desirable properties, such as closure under composition. In this paper, we accommodate the definition in a general regular category - which does not necessarily satisfy any form of axiom of choice. We show that this general definition 1) is closed under composition without using the axiom of choice, 2) coincides with other types of coalgebraic formulations under milder conditions, 3) coincides with the usual definition when the category has the regular axiom of choice. We then develop the particular case of toposes, where the formulation becomes nicer thanks to the power-object monad, and extend the formalism to simulations. Finally, we describe several examples in Stone spaces, toposes for name-passing, and modules over a ring.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Theory of computation → Semantics and reasoning
Keywords
  • Regular Categories
  • Toposes
  • Bisimulations
  • Coalgebra

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