Re: are sketches math objects?

["Zinovy Diskin" <zdiskin@swen.uwaterloo.ca>]

Yes, all this "discussion" is mainly misunderstanding, and I apologize
if I've contributed to it. It seems it was triggered by this piece:

On Wed, Sep 17, 2008 at 12:36 AM,  <Andre.Rodin@ens.fr> wrote:
> Dear Steve,
>
>> Sketches are not mathematical objects in their own right, in the same sense
>> that groups or spaces are.
>
> Of course, they are not.
>
...

So, the issue is closed. Still there is some point to mention, and I
again apologize if I'm peering into it too much. Our entire
mis-discussion is, perhaps, a result of two different attitudes. CT
favors and prefers to work in a presentation-free setting while
engineering applications are all about presentations; and this
mismatch may contribute to the disdain of CT from the practitioners'
side.  (Of course, this is not meant to anyhow diminish the elegance,
value and usefulness even for practical problems such concepts as
triple or classifying category :).

Zinovy

On Sun, Sep 21, 2008 at 7:55 PM, Steve Lack <s.lack@uws.edu.au> wrote:
> On 21/09/08 3:34 AM, "Zinovy Diskin" <zdiskin@swen.uwaterloo.ca> wrote:
>
>> Okay, sketches are presentations of theories but Steve's claim was
>> that they are not mathematical objects. Michael's and mine
>> bewilderment is about why does the former imply the latter?  (at
>> least, why "of course" :)
>>
>> Zinovy
>>
>
> What I actually said was this:
>
> "Sketches are not mathematical objects in their own right, in the same sense
> that groups or spaces are. They are presentations (for theories), and have
> status similar to other sorts of presentations (for groups, rings, etc.)
>
> Of course that is in no way meant to suggest that they are not important and
> worthy of study."
>
> So I did not say that "they are not mathematical objects", and I used the
> words "of course" only in clarifying that I was not suggesting that they
> were unimportant. What I was saying was that they have a different flavour
> to such mathematical objects as groups or spaces. I was saying this in
> response to the observation that sketches did not seem to fit into the
> Bourbaki notion of structure, and so in particular, that the notion of
> isomorphism of sketch was not as crucial as that of isomorphism of group.
>
> Michael Barr asked what the content of the statement might be. I certainly
> wasn't trying to make a precise mathematical statement, although Michael
> himself indicated one that could be made. I guess that my second sentence
> (that sketches are presentations) is the content. So the content, if you
> like, is "whatever status you give to group presentations, you should give
> the same to sketches". For my part, I think that presentations are extremely
> important technical tools, which need to be studied and understood; but
> which nonetheless are just that: technical tools for dealing with the real
> objects of study (the things they present).
>
> Steve Lack.
>
>