Sets for Mathematics

F. William Lawvere, Robert Rosebrugh

272 pages, parution le 22/04/2003

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Résumé

Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time in a text, this book 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

Abstract sets and mappings
Sums, monomorphisms and parts
Finite inverse limits
Colimits, epimorphisms and the axiom of choice
Mapping sets and exponentials
Summary of the axioms and an example of variable sets
Consequences and uses of exponentials
More on power sets
Introduction to variable sets
Models of additional variation

Appendixes
Bibliography
Index

L'auteur - F. William Lawvere

State University of New York at Buffalo

L'auteur - Robert Rosebrugh

Mount Allison University

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	F. William Lawvere, Robert Rosebrugh
Parution	22/04/2003
Nb. de pages	272
Format	17,7 x 25,3
Couverture	Broché
Poids	498g
Intérieur	Noir et Blanc
EAN13	9780521010603
ISBN13	978-0-521-01060-3