Sets for mathematics / F. William Lawvere, Robert Rosebrugh.

Format:

Book

Author/Creator:

Lawvere, F. W., author.

Rosebrugh, Robert, 1948- author.

Language:

English

Subjects (All):

Set theory.

Physical Description:

1 online resource (xiii, 261 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2003.

Language Note:

English

Summary:

Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. This book, first published in 2003, uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure of the axiom of choice. An appendix provides an explicit introduction to necessary concepts from logic, and an extensive glossary provides a window to the mathematical landscape.

Contents:

Cover; Half-title; Title; Copyright; Contents; Foreword; Contributors to Sets for Mathematics; 1 Abstract Sets and Mappings; 2 Sums, Monomorphisms, and Parts; 3 Finite Inverse Limits; 4 Colimits, Epimorphisms, and the Axiom of Choice; 5 Mapping Sets and Exponentials; 6 Summary of the Axioms and an Example of Variable Sets; 7 Consequences and Uses of Exponentials; 8 More on Power Sets; 9 Introduction to Variable Sets; 10 Models of Additional Variation; Appendix A Logic as the Algebra of Parts; Appendix B The Axiom of Choice and Maximal Principles

Appendix C Definitions, Symbols, and the Greek AlphabetBibliography; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 253-255) and index.

ISBN:

1-107-13104-9

0-511-64350-0

9786612387326

1-282-38732-4

0-511-07794-7

0-511-20554-6

0-511-56136-9

0-511-75546-5

0-511-07637-1

OCLC:

171136648