Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time, 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 that express universal properties of sums, products, mapping sets, and natural number recursion.


Editorial ReviewsReview"...the categorical approach to mathematics has never been presented with greater conviction than it has in this book. The authors show that the use of categories in analyzing the set concept is not only natural, but inevitable." Mathematical Reviews

"To learn set theory this way means not having to relearn it later.... Recommended." Choice

Book DescriptionAdvanced 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 andphysically common phenomena and advancing to a precise specification of the nature of Categories of Sets. An Appendix provides an explicit introduction to necessary concepts from logic, and an extensive Glossary provides a window to the mathematical landscape.

Product Details

• Paperback: 276 pages
• Publisher: Cambridge University Press; 1 edition (January 27, 2003)
• Language: English
• ISBN-10: 0521010608
• ISBN-13: 978-0521010603
  

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