In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra. Starting with intuitive descriptions of mathematically and physically common phenomena, it leads up to a precise specification of the Category of Sets. Suitable for advanced undergraduates and beginning graduate students.
In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra. Starting with intuitive descriptions of mathematically and physically common phenomena, it leads up to a precise specification of the Category of Sets. Suitable for advanced undergraduates and beginning graduate students.
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.
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.
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