Posted by
Carl Tollander on
Aug 13, 2008; 7:34pm
URL: http://friam.383.s1.nabble.com/Intro-tp687216p722632.html
John,
How do you feel about Goldblatt's book on Topoi? I've been working
through it slooowly and like it so far, but I'm not sure whether it is
leaving important things out. In particular, if you need something to
understand the exposition, say, sheaves, then he goes back and tells you
just enough about sheaves instead of referring you elsewhere.
Like this:
http://www.amazon.com/Topoi-Categorial-Analysis-Logic-Mathematics/dp/0486450260/ref=pd_bbs_2?ie=UTF8&s=books&qid=1218653851&sr=8-2When I try to talk to non-math-centric folks about Category Theory, I
usually start off with Derek Wise's "Stuff with Structure, having
certain Properties" based explanation, but usually people think its such
an advanced topic that such a starting point couldn't possibly be that
straightforward. If they do buy into that, however, you can give them a
feel for n-Cats and natural transformations. At that point they start
thinking what they could do with them and there's (maybe) enough
motivation to backfill in with the formal definitions. It's harder I
think to go with the formal stuff first (I know it is for me) if there
isn't much formal math background to relate to.
I think category theory (particularly for us as it relates to
complexity) represents a cultural change and so the initial explanations
we seek have to resonate broadly at that level if we are going to set a
foundation for not fooling ourselves (and our clients) when things get
more formal.
And I always liked the idea of using "stuff" as a technical term.
Carl
John F. Kennison wrote:
> Further thoughts on categories and their applications.
>
> References: Toposes. Theories and Triples can be found at Michael
> Barr’s home page, www.math.mcgill.ca/barr/. The notes suggested by
> Jochen, below, are a good starting point.
>
> Applications: There are a lot of different types of categories and
> categorical constructions. So there are, potentially, lots of possible
> applications. It is probably best to have a team approach, with at
> least one expert in the area of the intended application and at least
> one expert in category theory. But all experts have to learn something
> of the language, basic results, concepts of both fields, then they can
> see if one set of ideas can map onto another.
>
> This sort of provides an answer to Nick’s question. One can benefit
> (or perhaps enjoy) a field of abstract mathematics if the underlying
> concepts can be made intuitively clear with a minimum of technical
> complexity.
>
> Specifically can categories relate to questions of metaphor and
> analogy? Rosen in “Life Itself” belabors an approach to metaphor which
> strikes me as heavy-handed yet not comprehensive enough. Is there a
> better connection? --I think that’s a good question.
>
> --John
>
> On 8/12/08 3:39 PM, "Jochen Fromm" <
[hidden email]> wrote:
>
> I wonder if category theory can be applied
> to model metaphors and analogies? Or perhaps
> gene regulatory networks?
>
> The following slides seem to be suitable for folks
> with a good undergrad math background:
> "Category Theory for Beginners"
>
http://www.cs.toronto.edu/~sme/presentations/cat101.pdf> <
http://www.cs.toronto.edu/%7Esme/presentations/cat101.pdf>
>
> -J.
>
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FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at
http://www.friam.org