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Categories for Quantum TheoryAn Introduction$
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Chris Heunen and Jamie Vicary

Print publication date: 2019

Print ISBN-13: 9780198739623

Published to Oxford Scholarship Online: January 2020

DOI: 10.1093/oso/9780198739623.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 23 April 2021

Monoidal Categories

Monoidal Categories

(p.29) 1 Monoidal Categories
Categories for Quantum Theory

Chris Heunen

Jamie Vicary

Oxford University Press

A monoidal category is a category equipped with extra data, describing how objects and morphisms can be combined in parallel. This chapter introduces the theory of monoidal categories, including braidings, symmetries and coherence. They form the core of this book, as they provide the basic language with which the rest of the material will be developed. We introduce a visual notation called the graphical calculus, which provides an intuitive and powerful way to work with them. We also introduce the monoidal categories Hilb of Hilbert spaces and linear maps, Set of sets and functions and Rel of sets and relations, which will be used as running examples throughout the book.

Keywords:   Monoidal category, Tensor product, Coherence, Graphical calculus, States and effects, Braiding and symmetry

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