Sets for Mathematics [electronic resource].
 Responsibility
 F. William Lawvere, Robert Rosebrugh.
 Imprint
 Cambridge : Cambridge University Press, 2003.
 Physical description
 1 online resource (276 p.) : digital, PDF file(s).
Online
More options
Description
Creators/Contributors
 Contributor
 Lawvere, F. William.
 Rosebrugh, Robert.
Contents/Summary
 Contents

 Foreword
 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
 Appendices
 Bibliography.
 (source: Nielsen Book Data)
 Publisher's 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.
(source: Nielsen Book Data)
Subjects
 Subjects
 Set theory.
Bibliographic information
 Publication date
 2003
 Note
 Title from publishers bibliographic system (viewed on 26 Apr 2012).
 Note
 Also issued in print format.
 Format
 Mode of access: World Wide Web.
 ISBN
 9780511755460 (ebook)
 9780521804448 (hardback)