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Categories Without Sets?

  1. Dec 7, 2009 #1
    Does anyone know of a book on Category Theory that purposely attempts to teach category theory without explicitly basing it upon set theory?
  2. jcsd
  3. Dec 8, 2009 #2


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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.
    Last edited by a moderator: May 4, 2017
  4. Dec 8, 2009 #3
    Ah, yes, I see that MacLane's book does indeed include such a section; thank you!
  5. Dec 8, 2009 #4


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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?
  6. Dec 9, 2009 #5
    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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