Re: Category Theory for the Sciences

[Harley Eades III <harley.eades@gmail.com>]

Hi, Michael.

I thought I would mention one more thing.  I think that this book and other work
is just the beginning of a whole new area of applied CT.  Perhaps I am wrong.

However, there are a few groups of people working on new applications using
primarily CT.

For example, check out the recent work of John Baez:

http://math.ucr.edu/home/baez/networks/index.html

John and his students have been making progress studying network theory
and control theory using CT.  This includes electrical circuits and chemical 
reactions.

Also, check out the recent report 

"Report from Dagstuhl Perspectives Workshop 14182: Categorical Methods at the Crossroads”

http://vesta.informatik.rwth-aachen.de/opus/volltexte/2014/4618/pdf/dagrep_v004_i004_p049_s14182.pdf

This was a meeting to discuss using CT as the basis for math modeling and 
applied science.

Very best,
Harley

On Jan 29, 2015, at 8:41 AM, Harley Eades III <harley.eades@gmail.com> wrote:

> Hi, Michael.
> 
> On Jan 28, 2015, at 7:59 PM, Michael Barr <barr@math.mcgill.ca> wrote:
> 
>> A book of that name by David I. Spivak, Mathematics at MIT was recently 
>> published by the MIT Press.  Has anyone seen it?  Did it seem interesting. 
>> I wonder what kind of science outside of string theory would find CT 
>> useful.
> 
> I have been reading it a little here and there.  I find it interesting, and fun
> to read.
> 
> You can find an older draft of the book on the authors webpage:
> 
> http://math.mit.edu/~dspivak/CT4S.pdf
> 
> If you are curious.
> 
> The books is an introduction to CT, but with an eye towards applications in
> the sciences.
> 
> It is based, I think, on the intuition the author has obtained from his
> work on using category theory to study databases.  He uses these ideas to
> come up with a nice illustrative way to relate categorical — and other mathematical — 
> ideas to various scientific situations called ontology logs (ologs).  These are essentially
> database schemes or a diagrams in CT.  However, they are more informal.  Then given an
> olog we can talk about facts, which are just commutative diagrams.   You can see a bunch
> of examples in the book.  These ologs help take an application one has in mind and situate it
> so the categorical structure is illuminated.
> 
> I find it interesting.  I really like his chapter on spans where he uses them to model
> experiments and metrics. 
> 
> As for sciences he talks about computer science, information science, chemistry, physics,
> material sciences.  I can’t recall which others.  
> 
> Very best,
> Harley
> 
>> 
>> Michael
>> 


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