categories: Re: Model Theory and Category Theory

categories: Re: Model Theory and Category Theory

[Philip Scott]

Dear Jonathan:

There will be an upcoming workshop June 19-20 at the CRM (Centre de =20
Recherches Mathematiques) at the University
of Montreal, dedicated to Michael Makkai's 70th birthday, which is =20
exactly on this theme.  Its  local organizers
are Robert Seely and me, along with two model theorists (Bradd Hart =20
and Tommy Kucera), who were students of Makkai.

This was announced on this list some time ago, but a more up-to-date =20
announcement with the official CRM webpage will shortly be made
available from CRM.  I will post information soon.

										=
Cheers,
										=
Phil Scott

							=09



On 27-Jan-09, at 4:02 AM, Jonathan CHICHE =E9=BD=90=E6=AD=A3=E8=88=AA =
wrote:

> Hello,
>
> I am looking for references regarding the interplay between Model =20
> Theory and Category Theory. I came across an announcement related =20
> to this topic recently, possibly on this list, but I cannot find it =20=

> anymore. There has been a thread about it on the n-Category caf=C3=A9 =
a =20
> few months ago also. Do you have any other reference? What would be =20=

> the best place to start?
>
> Thanks in advance,
>
> Jonathan

categories: Re: Model Theory and Category Theory

[Colin McLarty]

So far as I know the most explicit, extensive account of how model
theorists do use categories---and ought to use them more freely and
explicitly---is in

  AUTHOR =       {Macintyre, Angus},
  TITLE =        {Model Theory: Geometrical and Set-Theoretic Aspects
and Prospects},
  JOURNAL =      {Bulletin of Symbolic Logic},
  YEAR =         {2003},
  volume =       {9},
  number =       {2},
  pages =        {197--212},


And there are some pointed remarks, about a tendency to avoid explicitly
using categorical tools that are in effect already being used, in
Pillay's part of

   Author =      {Buss, Samuel and Kechris, Alexander and Pillay, Anand
and Shore, Richard},
  TITLE =        {The Prospects for Mathematical Logic in the
Twenty-First Century},
  JOURNAL =      {Bulletin of Symbolic Logic},
  YEAR =         {2001},
  volume =       {7},
  number =       {2},
  pages =        {169--96},


Unsystematic uses occur throughout the literature, often without using
the word "category."  I would mention especially  

AUTHOR =       {van den Dries, Lou},
  TITLE =        {Tame Topology and O-minimal Structures},
  PUBLISHER =    {Cambridge University Press},
  YEAR =         {1998},
  address =      {Cambridge},

  editor =       {Haskell, Dierdre and Pillay, Anand and Steinhorn,
Charles},
  TITLE =        {Model Theory, Algebra, and Geometry},
  PUBLISHER =    {Cambridge University Press},
  YEAR =         {2000},
  number =       {39},
  series =       {Mathematical Sciences Research Center Publications},


best, Colin




----- Original Message -----
From: Jonathan CHICHE ??? <jonathan.chiche@polytechnique.edu>
Date: Tuesday, January 27, 2009 7:32 am
Subject: categories: Model Theory and Category Theory
To: Categories list <categories@mta.ca>

> Hello,
> 
> I am looking for references regarding the interplay between Model  
> Theory and Category Theory. I came across an announcement related 
> to  
> this topic recently, possibly on this list, but I cannot find it  
> anymore. There has been a thread about it on the n-Category café a  
> few months ago also. Do you have any other reference? What would be 
> 
> the best place to start?
> 
> Thanks in advance,
> 
> Jonathan 
> 
>