Topos Theory

Author: P.T. Johnstone

Publisher: Courier Corporation

ISBN: 0486493369

Category: Mathematics

Page: 400

View: 2007

Focusing on topos theory's integration of geometric and logical ideas into the foundations of mathematics and theoretical computer science, this volume explores internal category theory, topologies and sheaves, geometric morphisms, and other subjects. 1977 edition.

Toposes and Local Set Theories

An Introduction

Author: John L. Bell

Publisher: Courier Corporation

ISBN: 0486462862

Category: Mathematics

Page: 267

View: 5351

This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.

Abstract and Concrete Categories

The Joy of Cats

Author: Jiri Adamek,Jiří Adámek (ing.),Horst Herrlich,George E. Strecker

Publisher: N.A

ISBN: 9780486469348

Category: Mathematics

Page: 517

View: 8187

This up-to-date introductory treatment employs the language of category theory to explore the theory of structures. Its unique approach stresses concrete categories, and each categorical notion features several examples that clearly illustrate specific and general cases. A systematic view of factorization structures, this volume contains seven chapters. The first five focus on basic theory, and the final two explore more recent research results in the realm of concrete categories, cartesian closed categories, and quasitopoi. Suitable for advanced undergraduate and graduate students, it requires an elementary knowledge of set theory and can be used as a reference as well as a text. Updated by the authors in 2004, it offers a unifying perspective on earlier work and summarizes recent developments.

Elementary Categories, Elementary Toposes

Author: Colin McLarty

Publisher: Clarendon Press

ISBN: 9780191589492


Page: 278

View: 439

The book covers elementary aspects of category theory and topos theory. It has few mathematical prerequisites, and uses categorical methods throughout rather than beginning with set theoretic foundations. It works with key notions such as cartesian closedness, adjunctions, regular categories, and the internal logic of a topos. Full statements and elementary proofs are given for the central theorems, including the fundamental theorem of toposes, the sheafification theorem, and the construction of Grothendieck toposes over any topos as base. Three chapters discuss applications of toposes in detail, namely to sets, to basic differential geometry, and to recursive analysis. - ;Introduction; PART I: CATEGORIES: Rudimentary structures in a category; Products, equalizers, and their duals; Groups; Sub-objects, pullbacks, and limits; Relations; Cartesian closed categories; Product operators and others; PART II: THE CATEGORY OF CATEGORIES: Functors and categories; Natural transformations; Adjunctions; Slice categories; Mathematical foundations; PART III: TOPOSES: Basics; The internal language; A soundness proof for topos logic; From the internal language to the topos; The fundamental theorem; External semantics; Natural number objects; Categories in a topos; Topologies; PART IV: SOME TOPOSES: Sets; Synthetic differential geometry; The effective topos; Relations in regular categories; Further reading; Bibliography; Index. -

Number Theory

Author: George E. Andrews

Publisher: Courier Corporation

ISBN: 9780486682525

Category: Mathematics

Page: 259

View: 5167

Written by a distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.

Sketches of an Elephant: A Topos Theory Compendium

Author: P. T. Johnstone

Publisher: Oxford University Press

ISBN: 9780198515982

Category: Mathematics

Page: 716

View: 4003

Topos Theory is an important branch of mathematical logic of interest to theoretical computer scientists, logicians and philosophers who study the foundations of mathematics, and to those working in differential geometry and continuum physics. This compendium contains material that was previously available only in specialist journals. This is likely to become the standard reference work for all those interested in the subject.

Category Theory in Context

Author: Emily Riehl

Publisher: Courier Dover Publications

ISBN: 0486820807

Category: Mathematics

Page: 272

View: 8641

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.


The Categorial Analysis of Logic

Author: Robert Goldblatt

Publisher: Courier Corporation

ISBN: 048631796X

Category: Mathematics

Page: 576

View: 6279

A classic exposition of a branch of mathematical logic that uses category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers.

An Introduction to Category Theory

Author: Harold Simmons

Publisher: Cambridge University Press

ISBN: 1139503324

Category: Mathematics

Page: N.A

View: 3548

Category theory provides a general conceptual framework that has proved fruitful in subjects as diverse as geometry, topology, theoretical computer science and foundational mathematics. Here is a friendly, easy-to-read textbook that explains the fundamentals at a level suitable for newcomers to the subject. Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory. It gives the basic definitions; goes through the various associated gadgetry, such as functors, natural transformations, limits and colimits; and then explains adjunctions. The material is slowly developed using many examples and illustrations to illuminate the concepts explained. Over 200 exercises, with solutions available online, help the reader to access the subject and make the book ideal for self-study. It can also be used as a recommended text for a taught introductory course.

Introduction to Higher-Order Categorical Logic

Author: J. Lambek,P. J. Scott

Publisher: Cambridge University Press

ISBN: 9780521356534

Category: Mathematics

Page: 304

View: 7531

Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.

Categorical Logic and Type Theory

Author: Bart Jacobs

Publisher: Gulf Professional Publishing

ISBN: 9780444508539

Category: Mathematics

Page: 760

View: 1855

This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.

Algebraic Logic

Author: Paul R. Halmos

Publisher: Courier Dover Publications

ISBN: 0486810410

Category: Mathematics

Page: 272

View: 5750

Beginning with an introduction to the concepts of algebraic logic, this concise volume features ten articles by a prominent mathematician that originally appeared in journals from 1954 to 1959. Covering monadic and polyadic algebras, these articles are essentially self-contained and accessible to a general mathematical audience, requiring no specialized knowledge of algebra or logic. Part One addresses monadic algebras, with articles on general theory, representation, and freedom. Part Two explores polyadic algebras, progressing from general theory and terms to equality. Part Three offers three items on polyadic Boolean algebras, including a survey of predicates, terms, operations, and equality. The book concludes with an additional bibliography and index.

Introduction to Graph Theory

Author: Richard J. Trudeau

Publisher: Courier Corporation

ISBN: 0486318664

Category: Mathematics

Page: 224

View: 4044

Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.

Model Theory

Third Edition

Author: C.C. Chang,H. Jerome Keisler

Publisher: Courier Corporation

ISBN: 0486310957

Category: Mathematics

Page: 672

View: 1339

This bestselling textbook for higher-level courses was extensively revised in 1990 to accommodate developments in model theoretic methods. Topics include models constructed from constants, ultraproducts, and saturated and special models. 1990 edition.

A Book of Set Theory

Author: Charles C Pinter

Publisher: Courier Corporation

ISBN: 0486497089

Category: Mathematics

Page: 256

View: 6691

"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

Basic Category Theory

Author: Tom Leinster

Publisher: Cambridge University Press

ISBN: 1107044243

Category: Mathematics

Page: 190

View: 1211

A short introduction ideal for students learning category theory for the first time.

Concepts of Probability Theory

Second Revised Edition

Author: Paul E. Pfeiffer

Publisher: Courier Corporation

ISBN: 0486165663

Category: Mathematics

Page: 416

View: 5911

Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduates students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.

Concepts of Modern Mathematics

Author: Ian Stewart

Publisher: Courier Corporation

ISBN: 0486134954

Category: Mathematics

Page: 368

View: 3182

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.

Axiomatic Set Theory

Author: Patrick Suppes

Publisher: Courier Corporation

ISBN: 0486136876

Category: Mathematics

Page: 265

View: 2033

Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.

The Penrose Transform

Its Interaction with Representation Theory

Author: Robert J. Baston,Michael G. Eastwood

Publisher: Courier Dover Publications

ISBN: 0486816621

Category: Mathematics

Page: 256

View: 5754

Geared toward students of physics and mathematics; presupposes no familiarity with twistor theory. "A huge amount of information, well organized and condensed into less than 200 pages." — Mathematical Reviews. 1989 edition.