(Off-topic) Question about categories
alastair at reid-consulting-uk.ltd.uk
Thu Sep 18 18:02:06 EDT 2003
> But I'm hitting a mental block with this (and other places I've
> look don't add anything I can grok).
Two things I found useful when learning category theory are:
1) Try reading the definitions as though categories were just graphs:
Objects are nodes, morphisms are labelled edges and equality of morphism is
modulo some equivalence on lists of labels.
(Well, something like that - it's been a while since I played this game and
it's most useful for you to work out all the ins and outs of it yourself.)
2) Look for lots and lots of examples of categories.
Besides the obvious category of sets, there's domain theory (very useful to
help you get a handle on pushouts, initial, final, and the like), and lots
and lots of others. (Ask computer scientists for examples though - if you
have to learn topology before you can understand the categories that
mathematicians like to use, you won't gain much insight.)
Actually, these are just two different ways of saying to look beyond the
obvious Set category. The value of category theory is in its generalizations
and, especially, in its ability to draw parallels between many different
situations so looking at any one example for too long will tend to hold you
Alastair Reid www.haskell-consulting.com
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