Functors On The Category Of Hilbert Spaces
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Functors On The Category Of Hilbert Spaces
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Author : Jan Epema
language : en
Publisher:
Release Date : 1973
Functors On The Category Of Hilbert Spaces written by Jan Epema and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Functor theory categories.
Functors And Categories Of Banach Spaces
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Author : P.W. Michor
language : en
Publisher: Springer
Release Date : 2006-11-15
Functors And Categories Of Banach Spaces written by P.W. Michor and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Functors And Categories Of Banach Spaces
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Author : P W Michor
language : en
Publisher: Springer
Release Date : 2014-01-15
Functors And Categories Of Banach Spaces written by P W Michor and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Lecture Notes In Mathematics
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Author :
language : en
Publisher:
Release Date : 1964
Lecture Notes In Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Banach spaces categories.
Involutive Category Theory
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Author : Donald Yau
language : en
Publisher: Springer Nature
Release Date : 2020-11-30
Involutive Category Theory written by Donald Yau and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-30 with Mathematics categories.
This monograph introduces involutive categories and involutive operads, featuring applications to the GNS construction and algebraic quantum field theory. The author adopts an accessible approach for readers seeking an overview of involutive category theory, from the basics to cutting-edge applications. Additionally, the author’s own recent advances in the area are featured, never having appeared previously in the literature. The opening chapters offer an introduction to basic category theory, ideal for readers new to the area. Chapters three through five feature previously unpublished results on coherence and strictification of involutive categories and involutive monoidal categories, showcasing the author’s state-of-the-art research. Chapters on coherence of involutive symmetric monoidal categories, and categorical GNS construction follow. The last chapter covers involutive operads and lays important coherence foundations for applications to algebraic quantum field theory. With detailed explanations and exercises throughout, Involutive Category Theory is suitable for graduate seminars and independent study. Mathematicians and mathematical physicists who use involutive objects will also find this a valuable reference.
Banach Modules And Functors On Categories Of Banach Spaces
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Author : Johann Cigler
language : en
Publisher:
Release Date : 1979
Banach Modules And Functors On Categories Of Banach Spaces written by Johann Cigler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
Categories For Quantum Theory
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Author : Chris Heunen
language : en
Publisher: Oxford University Press
Release Date : 2019-11-14
Categories For Quantum Theory written by Chris Heunen and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-14 with Mathematics categories.
Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition, and a conceptual way to understand many high-level quantum phenomena. This text lays the foundation for this categorical quantum mechanics, with an emphasis on the graphical calculus which makes computation intuitive. Biproducts and dual objects are introduced and used to model superposition and entanglement, with quantum teleportation studied abstractly using these structures. Monoids, Frobenius structures and Hopf algebras are described, and it is shown how they can be used to model classical information and complementary observables. The CP construction, a categorical tool to describe probabilistic quantum systems, is also investigated. The last chapter introduces higher categories, surface diagrams and 2-Hilbert spaces, and shows how the language of duality in monoidal 2-categories can be used to reason about quantum protocols, including quantum teleportation and dense coding. Prior knowledge of linear algebra, quantum information or category theory would give an ideal background for studying this text, but it is not assumed, with essential background material given in a self-contained introductory chapter. Throughout the text links with many other areas are highlighted, such as representation theory, topology, quantum algebra, knot theory, and probability theory, and nonstandard models are presented, such as sets and relations. All results are stated rigorously, and full proofs are given as far as possible, making this book an invaluable reference for modern techniques in quantum logic, with much of the material not available in any other textbook.
Category Theory And Computer Science
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Author : Eugenio Moggi
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-08-20
Category Theory And Computer Science written by Eugenio Moggi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-20 with Computers categories.
This book constitutes the refereed proceedings of the 7th International Conference on Category Theory and Computer Science, CTCS'97, held in Santa Margheria Ligure, Italy, in September 1997. Category theory attracts interest in the theoretical computer science community because of its ability to establish connections between different areas in computer science and mathematics and to provide a few generic principles for organizing mathematical theories. This book presents a selection of 15 revised full papers together with three invited contributions. The topics addressed include reasoning principles for types, rewriting, program semantics, and structuring of logical systems.
Lectures And Exercises On Functional Analysis
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Author : Александр Яковлевич Хелемский
language : en
Publisher: American Mathematical Soc.
Release Date :
Lectures And Exercises On Functional Analysis written by Александр Яковлевич Хелемский and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces.
Quantum Symmetries For Quantum Spaces
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Author : Roberto Hernandez Palomares
language : en
Publisher:
Release Date : 2021
Quantum Symmetries For Quantum Spaces written by Roberto Hernandez Palomares and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Categories (Mathematics) categories.
This thesis consists of three self-contained papers from my graduate work at The Ohio State University. In Chapter 2, we introduce most of the necessary results, notation, techniques, and examples used in the reminder of this document, involving unitary tensor categories (UTC) and C*-2-categories. In Chapter 3 we introduce Q-Systems in a $\dag$-2-category and their bimodules, and define the Q-System completion of a $\dag$-2-category. We later prove $\rCorr,$ the C*-2-category of right C*-correspondences, is Q-System complete by constructing an inverse to the canonical embedding of $\rCorr$ into its Q-System completion $\QSys(\rCorr)$. In Chapter 4 we introduce generalized Temperley-Lieb-Jones ($\TLJ$) $\dag$-2-categories associated to weighted bidirected graphs, meant to represent lattices of inclusions of finite-index subfactors. We formally define unitary modules for these generalized $\TLJ$ $\dag$-2-categories as strong $\dag$-2-functors into $\BigHilb,$ the $\dag$-2-category of row-finite separable bigraded Hilbert spaces. We then classify these modules up to $\dag$-2-equivalence in terms of weighted bi-directed $\Gamma$-fair and balanced graphs, in the spirit of Yamagami's classification of fiber functors on $\TLJ(\delta)$ categories [Yam04], and De Commer and Yamashita's classification of unitary modules for ${\rm Rep(SU}_q(2))$ [DCY15]. In Chapter 5 we show that every UTC acts on some separable simple and monotracial C*-algebra, using diagrammatic, functional analytic and free probabilistic techniques. We construct a fully-faithful bi-involutive strong tensor functor onto a full subcategory of fgp bimodules over a simple exact separable unital monotracial C*-algebra. This C*-algebra is built solely from the category using the Guionnet-Jones-Shlyakhtenko construction introduced in [GJS11]. Proving the aforementioned properties of this functor involves a certain Hilbertification tensor functor, whose source is the UTC of finitely generated projective Hilbert C*-bimodules with certain tracial compatibilities, into the category of bi-finite spherical bimodules over an interpolated free group factor. The composite of these two functors recovers the UTC-action constructed in {BHP12].