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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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Monoidal Categories

Monoidal Categories

Chapter:
(p.29) 1 Monoidal Categories
Source:
Categories for Quantum Theory
Author(s):

Chris Heunen

Jamie Vicary

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198739623.003.0001

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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