#### CarlB

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Kea tells me that a good first book to read to learn category theory is

F. William Lawvere and Robert Rosebrugh

It is also available in hardback, but I have the paperback, linked above.

When I opened the book and read at random, I was briefly convinced that it wasn't telling me anything I didn't already know. All the usual undergraduate analysis is here. It just doesn't seem very difficult. On the other hand, Kea tells me that category theory has great possibilities for moving beyond the standard model.

This combination, ease of material, and power of use, make the book very attractive to me. You can be sure I will be reading it, and making comments here. Hopefully Kea will drop by and contribute to how this is related to braids and all that.

I can hardly wait to see what sort of connection there is between the axiom of choice and physics, though I always had my doubts about how physicists treated "infinity".

**Sets for Mathematics**$45F. William Lawvere and Robert Rosebrugh

*Advanced undergraduate or beginning graduate students need a unified foundation for their study of mathematics. For the first time in a text, 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 specifcation 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. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geomtry and analysis, are made explicit and taken as special axioms. Functor categories are introduced 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.https://www.amazon.com/dp/0521010608/?tag=pfamazon01-20Set 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. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geomtry and analysis, are made explicit and taken as special axioms. Functor categories are introduced 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.

It is also available in hardback, but I have the paperback, linked above.

When I opened the book and read at random, I was briefly convinced that it wasn't telling me anything I didn't already know. All the usual undergraduate analysis is here. It just doesn't seem very difficult. On the other hand, Kea tells me that category theory has great possibilities for moving beyond the standard model.

This combination, ease of material, and power of use, make the book very attractive to me. You can be sure I will be reading it, and making comments here. Hopefully Kea will drop by and contribute to how this is related to braids and all that.

I can hardly wait to see what sort of connection there is between the axiom of choice and physics, though I always had my doubts about how physicists treated "infinity".

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