Category Theory And Applications A Textbook For Beginners Second Edition
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Category Theory And Applications A Textbook For Beginners Second Edition
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Author : Marco Grandis
language : en
Publisher: World Scientific
Release Date : 2021-03-05
Category Theory And Applications A Textbook For Beginners Second Edition written by Marco Grandis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-05 with Mathematics categories.
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 And Applications
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Author : Marco Grandis
language : en
Publisher:
Release Date : 2018
Category Theory And Applications written by Marco Grandis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Categories (Mathematics) categories.
Basic Category Theory
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Author : Tom Leinster
language : en
Publisher: Cambridge University Press
Release Date : 2014-07-24
Basic Category Theory written by Tom Leinster and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-24 with Mathematics categories.
A short introduction ideal for students learning category theory for the first time.
Categories For The Working Mathematician
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Author : Saunders Mac Lane
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Categories For The Working Mathematician written by Saunders Mac Lane 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 2013-04-17 with Mathematics categories.
An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.
Category Theory In Context
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Author : Emily Riehl
language : en
Publisher: Courier Dover Publications
Release Date : 2017-03-09
Category Theory In Context written by Emily Riehl and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-09 with Mathematics categories.
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.
An Introduction To The Language Of Category Theory
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Author : Steven Roman
language : en
Publisher: Birkhäuser
Release Date : 2017-01-05
An Introduction To The Language Of Category Theory written by Steven Roman and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-05 with Mathematics categories.
This textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in university-level mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, step-by-step manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. The first chapter of the book introduces the definitions of category and functor and discusses diagrams,duality, initial and terminal objects, special types of morphisms, and some special types of categories,particularly comma categories and hom-set categories. Chapter 2 is devoted to functors and naturaltransformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions – products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts.
Basic Category Theory For Computer Scientists
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Author : Benjamin C. Pierce
language : en
Publisher: MIT Press
Release Date : 1991-08-07
Basic Category Theory For Computer Scientists written by Benjamin C. Pierce and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-08-07 with Computers categories.
Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading
Algebraic Topology A Structural Introduction
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Author : Marco Grandis
language : en
Publisher: World Scientific
Release Date : 2021-12-24
Algebraic Topology A Structural Introduction written by Marco Grandis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-24 with Mathematics categories.
Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying structural layout - the topics of Homological Algebra, Homotopy Theory and Category Theory which occur in its foundation.This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with a moderate amount of prerequisites — basic general topology and little else — and a moderate progression starting from a very elementary beginning. A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions.It can be used as a textbook for a semester course or self-study, and a guidebook for further study.
Category Theory
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Author : Steve Awodey
language : en
Publisher: Oxford University Press
Release Date : 2010-06-17
Category Theory written by Steve Awodey 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 2010-06-17 with Mathematics categories.
A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems (with full proofs), as well as numerous examples and exercises.
Category Theory
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Author : Steve Awodey
language : en
Publisher: OUP Oxford
Release Date : 2010-06-18
Category Theory written by Steve Awodey and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-18 with Philosophy categories.
Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership. Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists! This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.