Can You Recommend Books on Category Theory Without Set Theory?

[Reedeegi]

Does anyone know of a book on Category Theory that purposely attempts to teach category theory without explicitly basing it upon set theory?

 

[xristy]

See http://www.cs.man.ac.uk/~hsimmons/BOOKS/CatTheory.pdf" . Also the appendix on Foundations in MacLane's Categories for the Working Mathematician is a direct presentation.

 

[Reedeegi]

Ah, yes, I see that MacLane's book does indeed include such a section; thank you!

 

[Hurkyl]

What is the intent of your question? Maybe there are other interesting things out there you would find interesting -- topos theory comes to mind.

I know that someone (don't remember who) wrote a paper on directly axiomatizing the (super-large) 2-category of large categories, without reference to a formal set theory. Of course, his axioms provide for the construction of a large category Set, but I don't remember how that turns out to look. Maybe you'd find that interesting if you can find it?

 

[Reedeegi]

Yes, I've been able to track down and purchase books on topos theory; including Mac Lane's Sheaves in Geometry and Logic and Goldblatt's Topoi; also, that article you referenced may be Colin McLarty's one on axiomatizing the category of categories; does this ring a bell?