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Deconstructing Lawvere with distributive laws

Deconstructing Lawvere with distributive laws
Deconstructing Lawvere with distributive laws

PROs, PROPs and Lawvere categories are related notions adapted to the study of algebraic structures borne by an object in a category: PROs are monoidal, PROPs are symmetric monoidal and Lawvere categories are cartesian. This paper connects the three notions using Lack's technique for composing PRO(P)s via distributive laws. We show that Lawvere categories can be seen as the composite PROP CCm;T, where T expresses the algebraic structure in linear form and CCm express the ability of copying and discarding them. In turn the PROP T can be decomposed in terms of PROs as P;S where P expresses the ability of permuting variables and S is the PRO encoding the syntactic structure without permutations.

2352-2208
128-146
Bonchi, Filippo
3c53e89d-d280-4911-9938-eb861553d04e
Sobociński, Paweł
439334ab-2826-447b-9fe5-3928be3fd4fd
Zanasi, Fabio
5bc03cd7-0fb6-4e14-bae8-8bf0d5d4be38
Bonchi, Filippo
3c53e89d-d280-4911-9938-eb861553d04e
Sobociński, Paweł
439334ab-2826-447b-9fe5-3928be3fd4fd
Zanasi, Fabio
5bc03cd7-0fb6-4e14-bae8-8bf0d5d4be38

Bonchi, Filippo, Sobociński, Paweł and Zanasi, Fabio (2018) Deconstructing Lawvere with distributive laws. Journal of Logical and Algebraic Methods in Programming, 95, 128-146. (doi:10.1016/j.jlamp.2017.12.002).

Record type: Article

Abstract

PROs, PROPs and Lawvere categories are related notions adapted to the study of algebraic structures borne by an object in a category: PROs are monoidal, PROPs are symmetric monoidal and Lawvere categories are cartesian. This paper connects the three notions using Lack's technique for composing PRO(P)s via distributive laws. We show that Lawvere categories can be seen as the composite PROP CCm;T, where T expresses the algebraic structure in linear form and CCm express the ability of copying and discarding them. In turn the PROP T can be decomposed in terms of PROs as P;S where P expresses the ability of permuting variables and S is the PRO encoding the syntactic structure without permutations.

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More information

Accepted/In Press date: 2 December 2017
e-pub ahead of print date: 14 December 2017
Published date: 1 February 2018

Identifiers

Local EPrints ID: 418778
URI: https://eprints.soton.ac.uk/id/eprint/418778
ISSN: 2352-2208
PURE UUID: 330faacc-f4ea-431b-be89-623d23ca10ef

Catalogue record

Date deposited: 22 Mar 2018 17:30
Last modified: 13 Mar 2019 18:43

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