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From: Charles Wells <charles@abstractmath.org>
To: "Ellis D. Cooper" <xtalv1@netropolis.net>, catbb <categories@mta.ca>
Subject: Re: The Idea of Structure as Data and Conditions
Date: Sun, 27 May 2012 09:06:14 -0400	[thread overview]
Message-ID: <E1SYicp-0007ng-VC@mlist.mta.ca> (raw)
In-Reply-To: <CABZOOqZ54NtG1n3K4f8o6mMRSgZ_2yVjE6S+-UWkQSO_PXi1tQ@mail.gmail.com>

The sentence "contains all the info about any model" is ambiguous. I mean
the theory contains everything you can say that is correct about every
model. --C

On Sun, May 27, 2012 at 9:02 AM, Charles Wells <charles@abstractmath.org>wrote:

> Data and conditions constitute a presentation.  The graph, diagrams, cones
> & cocones of a sketch are a presentation.  This idea has not been
> superseded, not at all, but it has been completed (in two senses) by the
> concept of theory, which is the  object generated by the presentation: The
> theory of a sketch, the classifiying topos, the algebraic theory in the
> sense of Lawvere, and so on.  This object contains all the information
> about any model.
>
> That idea is in some way the other face of, or the complementary point of
> view about, data and conditions.
>
> Charles
>
>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]


  parent reply	other threads:[~2012-05-27 13:06 UTC|newest]

Thread overview: 11+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2012-05-25 22:09 Ellis D. Cooper
2012-05-26 23:48 ` Michael Barr
2012-05-27 18:16   ` Eduardo J. Dubuc
2012-05-28  6:00   ` FEJ Linton
2012-05-29 13:28     ` Staffan Angere
2012-05-30  6:26     ` Vaughan Pratt
2012-05-27 13:02 ` Charles Wells
     [not found] ` <CABZOOqZ54NtG1n3K4f8o6mMRSgZ_2yVjE6S+-UWkQSO_PXi1tQ@mail.gmail.com>
2012-05-27 13:06   ` Charles Wells [this message]
2012-05-27 23:25 ` Vaughan Pratt
2012-05-29  3:15 Fred E.J. Linton
2012-05-29 13:28 ` Colin McLarty

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