1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Categories Without Sets?

  1. Dec 7, 2009 #1

    Reedeegi

    User Avatar

    Does anyone know of a book on Category Theory that purposely attempts to teach category theory without explicitly basing it upon set theory?
     
    Reedeegi, Dec 7, 2009
  2. jcsd
    Phys.org - latest science and technology news stories on Phys.org
  3. Dec 8, 2009 #2

    xristy

    User Avatar
    Gold Member

    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
    xristy, Dec 8, 2009
  4. Dec 8, 2009 #3

    Reedeegi

    User Avatar

    Ah, yes, I see that MacLane's book does indeed include such a section; thank you!
     
    Reedeegi, Dec 8, 2009
  5. Dec 8, 2009 #4

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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?
     
    Hurkyl, Dec 8, 2009
  6. Dec 9, 2009 #5

    Reedeegi

    User Avatar

    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?
     
    Reedeegi, Dec 9, 2009
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Categories Without Sets?

  1. A World Without Time (Replies: 0)

  2. Books on Character theory and category theory (Replies: 2)

  3. Set theory (Replies: 10)

  4. Algebraic Topology via Categories (Replies: 5)

  5. Algebra text with category theory (Replies: 13)

Loading...