Jump to ContentJump to Main Navigation
Quantum Physics and LinguisticsA Compositional, Diagrammatic Discourse$
Users without a subscription are not able to see the full content.

Chris Heunen, Mehrnoosh Sadrzadeh, and Edward Grefenstette

Print publication date: 2013

Print ISBN-13: 9780199646296

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199646296.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 08 April 2020

Scalars, Monads, and Categories

Scalars, Monads, and Categories

Chapter:
(p.184) CHAPTER 7 Scalars, Monads, and Categories
Source:
Quantum Physics and Linguistics
Author(s):

Dion Coumans

Bart Jacobs

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199646296.003.0007

This chapter describes interrelations between: algebraic structure on sets of scalars, properties of monads associated with such sets of scalars, and structure in categories (especially Lawvere theories) associated with these monads. These interrelations will be expressed in terms of ‘triangles of adjunctions’, involving for instance various kinds of monoids (non-commutative, commutative, involutive) and semirings as scalars. It will be shown to which kind of monads and categories these algebraic structures correspond via adjunctions.

Keywords:   algebras on scalars, category theory, adjunction, Lawvere theories, monads, monoids, semirings

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .