task. Not sure why. Possibly just too elusive? Or possibly evolving
On Aug 13, 2008, at 1:58 PM, John F. Kennison wrote:
> Carl,
>
> I have only skimmed parts of Goldblatt's book. It did look like it
> was trying to do the hard job of giving the important concepts of
> topos theory, along with the basic technical details. (it is easier
> to assume that the readers know category theory and also know how to
> digest a book that only gives a formal approach to a subject.)
>
> Probably the best way to digest a new topic is to see how it applies
> to a particular problem, that is of interest. When I get organized
> (right now I am, teaching an intensive two-week course for incoming
> students who need a brushing up on pre-calculus, or pre-pre-calculus-
> and I also have a 12-year old granddaughter, who likes math, suduko
> and monopoly visiting until Tues.) --I might try to explain how I
> use topos theory to break a dynamic system into its cyclic parts.
>
> John
>
>
> On 8/13/08 3:36 PM, "Carl Tollander" <
[hidden email]> wrote:
>
> 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=books=1218653851=8-2
> <
http://www.amazon.com/Topoi-Categorial-Analysis-Logic-Mathematics/dp/0486450260/ref=pd_bbs_2?ie=UTF8&s=books&qid=1218653851&sr=8-2
> ><
http://www.amazon.com/Topoi-Categorial-Analysis-Logic-Mathematics/dp/0486450260/ref=pd_bbs_2?ie=UTF8&s=books&qid=1218653851&sr=8-2
> >
>
> When 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><
http://www.cs.toronto.edu/%7Esme/presentations/cat101.pdf
>> >
>>
>> -J.
>>
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>> Meets Fridays 9a-11:30 at cafe at St. John's College
>> lectures, archives, unsubscribe, maps at
http://www.friam.org>>
>>
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>>
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>> FRIAM Applied Complexity Group listserv
>> Meets Fridays 9a-11:30 at cafe at St. John's College
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http://www.friam.org>
>
> ============================================================
> 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>
>
> ============================================================
> 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.orgMeets Fridays 9a-11:30 at cafe at St. John's College