----- Original Message ----- From: "Graham Klyne" <[EMAIL PROTECTED]> To: "Haskell Cafe" <[EMAIL PROTECTED]> Sent: Thursday, September 18, 2003 9:44 AM Subject: (Off-topic) Question about categories
> (I'm asking here because I believe there is some overlap between category > theory and functional programming cognoscenti...) > > It has been suggested to me that categories may be a useful framework (more > useful than set theory) for conceptualizing things for which there is no > well-defined equality relationship. (The discussion is about resources in > WWW.) I've done a little digging about category theory, and find some > relatively approachable material at: > http://www.wikipedia.org/wiki/Category_theory > http://www.wikipedia.org/wiki/Class_(set_theory) > and nearby. > > But I'm hitting a mental block with this (and other places I've look don't > add anything I can grok). The definition of a category depends on the > definition of a morphism, and in particular the existence of an identity > morphism for every object in a category. The definition of an morphism is > in terms of equality of compositions of morphisms: > for f : A -> B we have Id[B]. f = f = f . Id[A] > > My problem is this: how does it make sense to define an equality of > morphisms without some well-defined concept of equality on the underlying > objects to which they apply? That is, given object X and an object Y, it > is possible to examine them and determine whether or not they are the same > object. And if the underlying objects have such a concept of equality, > what prevents them from being sets or members of sets? But categories are > presented as being more general than sets. > > Does anyone see the cause of my non-comprehension here? > > #g > > > ------------ > Graham Klyne > [EMAIL PROTECTED] Hi, There's some additional links about category theory in this LtU discussion: http://lambda.weblogs.com/discuss/msgReader$979. Also there's this presentation "Category Theory for Beginners" http://www.cs.toronto.edu/~sme/presentations/cat101.pdf. HTH. Best regards, Daniel Yokomiso. "Honesty is the best policy, but insanity is a better defense." --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com). Version: 6.0.518 / Virus Database: 316 - Release Date: 12/9/2003 _______________________________________________ Haskell-Cafe mailing list [EMAIL PROTECTED] http://www.haskell.org/mailman/listinfo/haskell-cafe
