Involutive Category Theory

Download Involutive Category Theory full books in PDF, epub, and Kindle. Read online Involutive Category Theory ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Involutive Category Theory

Author : Donald Yau
Publisher : Springer Nature
ISBN 13 : 3030612031
Total Pages : 250 pages
Book Rating : 4.0/5 (36 download)

DOWNLOAD NOW!

Book Synopsis Involutive Category Theory by : Donald Yau

Download or read book Involutive Category Theory written by Donald Yau and published by Springer Nature. This book was released on 2020-11-30 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Chapters three through five feature previously unpublished results on coherence and strictification of involutive categories and involutive monoidal categories, showcasing the author’s state-of-the-art research.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.

Category Theory

Author : Steve Awodey
Publisher : Oxford University Press
ISBN 13 : 0191513822
Total Pages : 269 pages
Book Rating : 4.1/5 (915 download)

DOWNLOAD NOW!

Book Synopsis Category Theory by : Steve Awodey

Download or read book Category Theory written by Steve Awodey and published by Oxford University Press. This book was released on 2006-05 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing example exercises, this reference to category theory is suitable for researchers and graduates in philosophy, mathematics, and computer science. With definitions of concepts, and proofs of propositions and theorems, the text makes the ideas of this topic understandable to the broad readership.

Elements of ∞-Category Theory

Author : Emily Riehl
Publisher : Cambridge University Press
ISBN 13 : 1108952194
Total Pages : 782 pages
Book Rating : 4.1/5 (89 download)

DOWNLOAD NOW!

Book Synopsis Elements of ∞-Category Theory by : Emily Riehl

Download or read book Elements of ∞-Category Theory written by Emily Riehl and published by Cambridge University Press. This book was released on 2022-02-10 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.

Category Theory And Applications: A Textbook For Beginners (Second Edition)

Author : Marco Grandis
Publisher : World Scientific
ISBN 13 : 9811236100
Total Pages : 390 pages
Book Rating : 4.8/5 (112 download)

DOWNLOAD NOW!

Book Synopsis Category Theory And Applications: A Textbook For Beginners (Second Edition) by : Marco Grandis

Download or read book Category Theory And Applications: A Textbook For Beginners (Second Edition) written by Marco Grandis and published by World Scientific. This book was released on 2021-03-05 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.

Category Theory in Context

Author : Emily Riehl
Publisher : Courier Dover Publications
ISBN 13 : 0486820807
Total Pages : 273 pages
Book Rating : 4.4/5 (868 download)

DOWNLOAD NOW!

Book Synopsis Category Theory in Context by : Emily Riehl

Download or read book Category Theory in Context written by Emily Riehl and published by Courier Dover Publications. This book was released on 2017-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Category Theory

Author : Horst Herrlich
Publisher : Addison Wesley Publishing Company
ISBN 13 :
Total Pages : 430 pages
Book Rating : 4.F/5 ( download)

DOWNLOAD NOW!

Book Synopsis Category Theory by : Horst Herrlich

Download or read book Category Theory written by Horst Herrlich and published by Addison Wesley Publishing Company. This book was released on 1973 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tensor Categories

Author : Pavel Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 1470434415
Total Pages : 362 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis Tensor Categories by : Pavel Etingof

Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.

Involutions on Manifolds

Author : Santiago Lopez de Medrano
Publisher : Springer Science & Business Media
ISBN 13 : 3642650120
Total Pages : 114 pages
Book Rating : 4.6/5 (426 download)

DOWNLOAD NOW!

Book Synopsis Involutions on Manifolds by : Santiago Lopez de Medrano

Download or read book Involutions on Manifolds written by Santiago Lopez de Medrano and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the results of work done during the years 1967-1970 on fixed-point-free involutions on manifolds, and is an enlarged version of the author's doctoral dissertation [54J written under the direction of Professor William Browder. The subject of fixed-paint-free involutions, as part of the subject of group actions on manifolds, has been an important source of problems, examples and ideas in topology for the last four decades, and receives renewed attention every time a new technical development suggests new questions and methods ([62, 8, 24, 63J). Here we consider mainly those properties of fixed-point-free involutions that can be best studied using the techniques of surgery on manifolds. This approach to the subject was initiated by Browder and Livesay. Special attention is given here to involutions of homotopy spheres, but even for this particular case, a more general theory is very useful. Two important related topics that we do not touch here are those of involutions with fixed points, and the relationship between fixed-point-free involutions and free Sl-actions. For these topics, the reader is referred to [23J, and to [33J, [61J, [82J, respectively. The two main problems we attack are those of classification of involutions, and the existence and uniqueness of invariant submanifolds with certain properties. As will be seen, these problems are closely related. If (T, l'n) is a fixed-point-free involution of a homotopy sphere l'n, the quotient l'n/Tis called a homotopy projective space.

Category Theory 1991: Proceedings of the 1991 Summer Category Theory Meeting, Montreal, Canada

Author : Robert Andrew George Seely
Publisher : American Mathematical Soc.
ISBN 13 : 9780821860182
Total Pages : 462 pages
Book Rating : 4.8/5 (61 download)

DOWNLOAD NOW!

Book Synopsis Category Theory 1991: Proceedings of the 1991 Summer Category Theory Meeting, Montreal, Canada by : Robert Andrew George Seely

Download or read book Category Theory 1991: Proceedings of the 1991 Summer Category Theory Meeting, Montreal, Canada written by Robert Andrew George Seely and published by American Mathematical Soc.. This book was released on 1992 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representing this diversity of the field, this book contains the proceedings of an international conference on category theory. The subjects covered here range from topology and geometry to logic and theoretical computer science, from homotopy to braids and conformal field theory. Although generally aimed at experts in the various fields represented, the book will also provide an excellent opportunity for nonexperts to get a feel for the diversity of current applications of category theory.

Category Theory in Physics, Mathematics, and Philosophy

Author : Marek Kuś
Publisher : Springer Nature
ISBN 13 : 3030308960
Total Pages : 134 pages
Book Rating : 4.0/5 (33 download)

DOWNLOAD NOW!

Book Synopsis Category Theory in Physics, Mathematics, and Philosophy by : Marek Kuś

Download or read book Category Theory in Physics, Mathematics, and Philosophy written by Marek Kuś and published by Springer Nature. This book was released on 2019-11-11 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to processes. The book approaches formal ontology in the original sense put forward by the philosopher Edmund Husserl, namely as a science that deals with entities that can be exemplified in all spheres and domains of reality. It is a dynamic, processual, and non-substantial ontology in which all entities can be treated as transformations, and in which objects are merely the sources and aims of these transformations. Thus, in a rather surprising way, when employed as a formal ontology, category theory can unite seemingly disparate disciplines in contemporary science and the humanities, such as physics, mathematics and philosophy, but also computer and complex systems science.

Category Theory And Applications: A Textbook For Beginners

Author : Marco Grandis
Publisher : World Scientific
ISBN 13 : 9813231084
Total Pages : 305 pages
Book Rating : 4.8/5 (132 download)

DOWNLOAD NOW!

Book Synopsis Category Theory And Applications: A Textbook For Beginners by : Marco Grandis

Download or read book Category Theory And Applications: A Textbook For Beginners written by Marco Grandis and published by World Scientific. This book was released on 2018-01-16 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a deeper understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers its basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications and a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.

What is Category Theory?

Author : Giandomenico Sica
Publisher : Polimetrica s.a.s.
ISBN 13 : 8876990313
Total Pages : 292 pages
Book Rating : 4.8/5 (769 download)

DOWNLOAD NOW!

Book Synopsis What is Category Theory? by : Giandomenico Sica

Download or read book What is Category Theory? written by Giandomenico Sica and published by Polimetrica s.a.s.. This book was released on 2006 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Categories for Quantum Theory

Author : Chris Heunen
Publisher : Oxford University Press
ISBN 13 : 0191060062
Total Pages : 320 pages
Book Rating : 4.1/5 (91 download)

DOWNLOAD NOW!

Book Synopsis Categories for Quantum Theory by : Chris Heunen

Download or read book Categories for Quantum Theory written by Chris Heunen and published by Oxford University Press. This book was released on 2019-11-14 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Basic Concepts of Enriched Category Theory

Author : Gregory Maxwell Kelly
Publisher : CUP Archive
ISBN 13 : 9780521287029
Total Pages : 260 pages
Book Rating : 4.2/5 (87 download)

DOWNLOAD NOW!

Book Synopsis Basic Concepts of Enriched Category Theory by : Gregory Maxwell Kelly

Download or read book Basic Concepts of Enriched Category Theory written by Gregory Maxwell Kelly and published by CUP Archive. This book was released on 1982-02-18 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Invitation to Applied Category Theory

Author : Brendan Fong
Publisher : Cambridge University Press
ISBN 13 : 1108582249
Total Pages : 351 pages
Book Rating : 4.1/5 (85 download)

DOWNLOAD NOW!

Book Synopsis An Invitation to Applied Category Theory by : Brendan Fong

Download or read book An Invitation to Applied Category Theory written by Brendan Fong and published by Cambridge University Press. This book was released on 2019-07-18 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.

The Theory of Quantaloids

Author : K I Rosenthal
Publisher : CRC Press
ISBN 13 : 1498710409
Total Pages : 176 pages
Book Rating : 4.4/5 (987 download)

DOWNLOAD NOW!

Book Synopsis The Theory of Quantaloids by : K I Rosenthal

Download or read book The Theory of Quantaloids written by K I Rosenthal and published by CRC Press. This book was released on 2014-07-22 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed account of the theory of quantaloids, a natural generalization of quantales. The basic theory, examples and construction are given and particular emphasis is placed on the free quantaloid construction, as well as on the perspective provided by enriched categories.

Starting Category Theory

Author : Paolo Perrone
Publisher : World Scientific
ISBN 13 : 9811286027
Total Pages : 464 pages
Book Rating : 4.8/5 (112 download)

DOWNLOAD NOW!

Book Synopsis Starting Category Theory by : Paolo Perrone

Download or read book Starting Category Theory written by Paolo Perrone and published by World Scientific. This book was released on 2024-04-08 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the central highlights of this work is the exploration of the Yoneda lemma and its profound implications, during which intuitive explanations are provided, as well as detailed proofs, and specific examples. This book covers aspects of category theory often considered advanced in a clear and intuitive way, with rigorous mathematical proofs. It investigates universal properties, coherence, the relationship between categories and graphs, and treats monads and comonads on an equal footing, providing theorems, interpretations and concrete examples. Finally, this text contains an introduction to monoidal categories and to strong and commutative monads, which are essential tools in current research but seldom found in other textbooks.Starting Category Theory serves as an accessible and comprehensive introduction to the fundamental concepts of category theory. Originally crafted as lecture notes for an undergraduate course, it has been developed to be equally well-suited for individuals pursuing self-study. Most crucially, it deliberately caters to those who are new to category theory, not requiring readers to have a background in pure mathematics, but only a basic understanding of linear algebra.