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Composition and Recursion for Causal Structures

Authors Henning Basold , Tanjona Ralaivaosaona

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Author Details

Henning Basold
  • LIACS, Leiden University, The Netherlands
Tanjona Ralaivaosaona
  • LIACS, Leiden University, The Netherlands

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Henning Basold and Tanjona Ralaivaosaona. Composition and Recursion for Causal Structures. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.CALCO.2023.18

Abstract

Causality appears in various contexts as a property where present behaviour can only depend on past events, but not on future events. In this paper, we compare three different notions of causality that capture the idea of causality in the form of restrictions on morphisms between coinductively defined structures, such as final coalgebras and chains, in fairly general categories. We then focus on one presentation and show that it gives rise to a traced symmetric monoidal category of causal morphisms. This shows that causal morphisms are closed under sequential and parallel composition and, crucially, under recursion.

Subject Classification

ACM Subject Classification
  • Theory of computation → Categorical semantics
Keywords
  • Causal morphisms
  • Final Coalgebras
  • Final Chains
  • Metric Maps
  • Guarded Recursion
  • Traced Symmetric Monoidal Category

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