Axiomatic Method and Category Theory

Axiomatic Method and Category Theory

[andrei rodin]

Dear List,

here is my newly published monograph on the history and philosophy of category theory and some other related matters:

http://www.springer.com/philosophy/book/978-3-319-00403-7
http://www.amazon.com/Axiomatic-Method-Category-Synthese-Library/dp/3319004034 


The main thesis of the book: Categorical logic brings us back to Euclid leaving Hilbert at the margins (I'm talking here about Hilbert's version of axiomatic method, not about his legacy as a whole). 

Table of Contents (Category theory doesn't appear in the book before Chapter 4):
Introduction.- Part I A Brief History of the Axiomatic Method.- Chapter 1. Euclid: Doing and Showing.- Chapter 2. Hilbert: Making It Formal.- Chapter 3. Formal Axiomatic Method and the 20th Century Mathematics.- Chapter. 4 Lawvere: Pursuit of Objectivity.- Conclusion of Part 1.- Part II. Identity and Categorification.- Chapter 5. Identity in Classical and Constructive Mathematics.- Chapter 6. Identity Through Change, Category Theory and Homotopy Theory.- Conclusion of Part 2.- Part III. Subjective Intuitions and Objective Structures.- Chapter 7. How Mathematical Concepts Get Their Bodies. Chapter 8. Categories versus Structures.- Chapter 9. New Axiomatic Method (instead of conclusion).- Bibliography.​

A draft version is on arXiv. I hope some of you may enjoy it and I'll be most grateful for any critique and any comment. 

best regards,
AR




[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Axiomatic Method and Category Theory

[andrei rodin]

>> A draft version is on arXiv. I hope some of you may enjoy it and I'll be most grateful for any critique and any comment.
>> 
>> best regards,
>> AR
>> 
>> 
>> 
>> 
> To help us (the lazy ones) find it can you give the explicit link to the arXive draft. Thanks, e.d.
> 

sure, here it is: http://arxiv.org/abs/1210.1478

by the way:  I'm subscribed to the list through a different email address: not andrei@philomatica.org but rodin@ens.fr  ; in fact I use both. AR
 






[For admin and other information see: http://www.mta.ca/~cat-dist/ ]