Introduction 1 10 free; Chapter 1. A division algebra is a central simple algebra 5 14 free; Chapter 2. Azumaya algebras at the generic point 11 20; Chapter 3. The Brauer group 20 29; Chapter 4. Form of matrices 27 36; Chapter 5. Torsion question 32 41; Chapter 6. Galois extensions 37 46; Chapter 7. Crossed products and cohomology 44 53; Chapter 8. Corestriction 55 64.
My question is obvious from the title of this post-what is, in your opinion, the best book for learning category theory for a person with my background in mathematics?As regards my background in math, I have an undergrad degree in mathematics. I have also independently studied the ZFC axioms using Suppe's book 'Axiomatic Set Theory.' I have not attended graduate school in math (I opted to go straight to the private sector, for better or worse), but I nonetheless want to extend my understanding of mathematics.Thanks for your recommendations!. One possibility is by Lawvere and Rosebrugh.
It's not about category theory per se, as used in algebra, but about a formulation of set theory in terms of category theory. So it is more concerned with logic and foundations than with algebra. Lawvere is a major contributor to category theory, especially topos theory.
The book is a little bit evangelical, as he promotes his view that category theory is a more natural foundation for set theory and the rest of mathematics than something like ZFC. But maybe he's right.
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January 2023
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