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International Colloquium on Theoretical Aspects of Computing

ICTAC 2018: Theoretical Aspects of Computing – ICTAC 2018 pp 116–131Cite as

Monoidal Multiplexing

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11187))

Abstract

Given a classical algebraic structure—e.g. a monoid or group—with carrier set X, and given a positive integer n, there is a canonical way of obtaining the same structure on carrier set \(X^n\) by defining the required operations “pointwise”. For resource-sensitive algebra (i.e. based on mere symmetric monoidal, not cartesian structure), similar “pointwise” operations are usually defined as a kind of syntactic sugar: for example, given a comonoid structure on X, one obtains a comultiplication on \(X\otimes X\) by tensoring two comultiplications and composing with an appropriate permutation. This is a specific example of a general construction that we identify and refer to as multiplexing. We obtain a general theorem that guarantees that any equation that holds in the base case will hold also for the multiplexed operations, thus generalising the “pointwise” definitions of classical universal algebra.

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Author information

Authors and Affiliations

  1. School of Electronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, UK

    Apiwat Chantawibul & Paweł Sobociński

Authors
  1. Apiwat Chantawibul
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  2. Paweł Sobociński
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Correspondence to Apiwat Chantawibul .

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Editors and Affiliations

  1. Stellenbosch University, Stellenbosch, South Africa

    Bernd Fischer

  2. Reykjavík University, Reykjavik, Iceland

    Tarmo Uustalu

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Chantawibul, A., Sobociński, P. (2018). Monoidal Multiplexing. In: Fischer, B., Uustalu, T. (eds) Theoretical Aspects of Computing – ICTAC 2018. ICTAC 2018. Lecture Notes in Computer Science(), vol 11187. Springer, Cham. https://doi.org/10.1007/978-3-030-02508-3_7

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  • DOI: https://doi.org/10.1007/978-3-030-02508-3_7

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  • Print ISBN: 978-3-030-02507-6

  • Online ISBN: 978-3-030-02508-3

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