Sets for Mathematics
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Sets for Mathematics by F. William Lawvere
Book DescriptionAdvanced 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.
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Book DetailsISBN: 9780521010603
(247mm x 174mm x 15mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 27-Jan-2003
Country of Publication: United Kingdom
Books By Author F. William Lawvere
Conceptual Mathematics, Paperback (July 2009)
This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.
Sets for Mathematics, Hardback (January 2003)» View all books by F. William Lawvere
In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
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