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Monoidal multiplexing

Monoidal multiplexing
Monoidal multiplexing
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 Xn 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⊗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.
116-131
Springer
Chantawibul, Apiwat
c5f42d94-3195-43d7-b6c1-ed67f60996f8
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Fischer, B.
Uustalu, T.
Chantawibul, Apiwat
c5f42d94-3195-43d7-b6c1-ed67f60996f8
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Fischer, B.
Uustalu, T.

Chantawibul, Apiwat and Sobocinski, Pawel (2018) Monoidal multiplexing. Fischer, B. and Uustalu, T. (eds.) In Theoretical Aspects of Computing – ICTAC 2018. vol. 11187, Springer. pp. 116-131 . (doi:10.1007/978-3-030-02508-3_7).

Record type: Conference or Workshop Item (Paper)

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 Xn 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⊗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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More information

e-pub ahead of print date: 15 October 2018
Venue - Dates: 15th International Colloquium on Theoretical Aspects of Computing<br/>12-19 October 2018, Stellenbosch, South Africa, 2018-10-16 - 2018-10-19

Identifiers

Local EPrints ID: 422947
URI: http://eprints.soton.ac.uk/id/eprint/422947
PURE UUID: bfa17e7b-36ef-4b93-9f9b-f41109ff2b98

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Date deposited: 08 Aug 2018 16:30
Last modified: 26 Nov 2021 06:28

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Contributors

Author: Apiwat Chantawibul
Author: Pawel Sobocinski
Editor: B. Fischer
Editor: T. Uustalu

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