Description: Sets for Mathematics In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra. F. William Lawvere (Author), Robert Rosebrugh (Author) 9780521804448, Cambridge University Press Hardback, published 20 January 2003 276 pages 26.3 x 18.2 x 2.1 cm, 0.65 kg "To learn set theory this way means not having to relearn it later.... Recommended." Choice 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. 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. Subject Areas: Set theory [PBCH], Mathematical foundations [PBC]
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BIC Subject Area 1: Set theory [PBCH]
BIC Subject Area 2: Mathematical foundations [PBC]
Item Height: 263 mm
Item Width: 182 mm
Author: F. William Lawvere, Robert Rosebrugh
Publication Name: Sets for Mathematics
Format: Hardcover
Language: English
Publisher: Cambridge University Press
Subject: Mathematics
Publication Year: 2003
Type: Textbook
Item Weight: 650 g
Number of Pages: 276 Pages
