Categories Without Sets?

  • Thread starter Reedeegi
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  • #1
Reedeegi
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Does anyone know of a book on Category Theory that purposely attempts to teach category theory without explicitly basing it upon set theory?
 

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  • #2
xristy
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See http://www.cs.man.ac.uk/~hsimmons/BOOKS/CatTheory.pdf" [Broken]. Also the appendix on Foundations in MacLane's Categories for the Working Mathematician is a direct presentation.
 
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  • #3
Reedeegi
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Ah, yes, I see that MacLane's book does indeed include such a section; thank you!
 
  • #4
Hurkyl
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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?
 
  • #5
Reedeegi
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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?
 

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