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Quantum Physics and LinguisticsA Compositional, Diagrammatic Discourse$
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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

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Scalars, Monads, and Categories

Scalars, Monads, and Categories

(p.184) CHAPTER 7 Scalars, Monads, and Categories
Quantum Physics and Linguistics

Dion Coumans

Bart Jacobs

Oxford University Press

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

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