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Vladimir_Nesov comments on Open thread, May 17-31 2013 - Less Wrong Discussion

2 [deleted] 17 May 2013 01:47PM

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Comment author: Vladimir_Nesov 24 May 2013 11:06:46PM *  5 points [-]

These texts can work as an introductory undergraduate sequence (with "Sets for Mathematics" going after enough exposure to rigor, e.g. a real analysis course, maybe some set theory and logic, and Awodey's book after a bit of abstract algebra, maybe functional programming with types, as in Haskell/Standard ML/etc.):

  • F. W. Lawvere & S. H. Schanuel (1991). Conceptual Mathematics: A First Introduction to Categories. Buffalo Workshop Press, Buffalo, NY, USA.
  • F. W. Lawvere & R. Rosebrugh (2003). Sets for Mathematics. Cambridge University Press.
  • S. Awodey (2006). Category Theory. Oxford Logic Guides. Oxford University Press, USA.
Comment author: Qiaochu_Yuan 26 May 2013 12:16:02AM 4 points [-]

Second the recommendation of Lawvere and Schanuel. It really communicates the categorical way of thinking without requiring a lot of mathematical background (more traditional texts on category theory will talk about things like algebraic topology which historically motivated category theory but aren't conceptually prior to it).

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