eprintid: 10046407
rev_number: 19
eprint_status: archive
userid: 608
dir: disk0/10/04/64/07
datestamp: 2018-04-11 15:20:29
lastmod: 2021-09-20 22:15:40
status_changed: 2018-04-11 15:20:29
type: article
metadata_visibility: show
creators_name: Bonchi, F
creators_name: Sobocinski, P
creators_name: Zanasi, F
title: Deconstructing Lawvere with distributive laws
ispublished: pub
divisions: UCL
divisions: B04
divisions: C05
divisions: F48
keywords: Science & Technology, Technology, Computer Science, Theory & Methods, Logic, Computer Science, Science & Technology - Other Topics, MONOIDAL CATEGORIES, ALGEBRA, MONADS, GRAPHS
note: © 2017 Elsevier Inc. All rights reserved. This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
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 , where  expresses the algebraic structure in linear form and  express the ability of copying and discarding them. In turn the PROP  can be decomposed in terms of PROs as  where expresses the ability of permuting variables and  is the PRO encoding the syntactic structure without permutations.
date: 2018-02
date_type: published
publisher: ELSEVIER SCIENCE INC
official_url: http://doi.org/10.1016/j.jlamp.2017.12.002
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
article_type_text: Article
verified: verified_manual
elements_id: 1540501
doi: 10.1016/j.jlamp.2017.12.002
lyricists_name: Zanasi, Fabio
lyricists_id: FZANA74
actors_name: Zanasi, Fabio
actors_name: Turnbull, Sarah
actors_id: FZANA74
actors_id: SLTUR91
actors_role: owner
actors_role: impersonator
full_text_status: public
publication: Journal of Logical and Algebraic Methods in Programming
volume: 95
pagerange: 128-146
pages: 19
issn: 2352-2208
citation:        Bonchi, F;    Sobocinski, P;    Zanasi, F;      (2018)    Deconstructing Lawvere with distributive laws.                   Journal of Logical and Algebraic Methods in Programming , 95    pp. 128-146.    10.1016/j.jlamp.2017.12.002 <https://doi.org/10.1016/j.jlamp.2017.12.002>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10046407/1/main.pdf