Umfang:
xiii, 261 Seiten
Ausgabe:
Online-Ausgabe Cambridge Cambridge University Press [July 2010] 1 Online-Ressource (xiii, 261 Seiten)
ISBN:
9780511755460
Inhalt:
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
Anmerkung:
Literaturverzeichnis: Seite 253-255
Weitere Ausg.:
ISBN 9780521804448
Weitere Ausg.:
ISBN 9780521010603
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe ISBN 9780521804448
Weitere Ausg.:
Elektronische Reproduktion von Lawvere, Francis W., 1937 - 2023 Sets for mathematics Cambridge [u.a.] : Cambridge Univ. Press, 2003 ISBN 0521804442
Weitere Ausg.:
ISBN 0521010608
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Mengenlehre
;
Kategorientheorie
;
Mengenlehre
;
Lehrbuch
;
Bibliografie
DOI:
10.1017/CBO9780511755460
URL:
Volltext
(lizenzpflichtig)
Mehr zum Autor:
Lawvere, Francis W. 1937-2023
