Re: Bourbaki and Categories

[Andre.Rodin@ens.fr]

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.


>They are presentations (for theories), and have
> status similar to other sorts of presentations (for groups, rings, etc.)


I think about a sketch as an alternative to a string of formulae, which
represents (axioms of) a theory. I didn't try to compare sketch theory with
group theory.  I tried to compare sketch theory with the general setting, in
which group theory is developed a la Bourbaki (along with many other
theories). A classical account of this general setting (which differs at certain
points with Bourbaki's version) is Tarski's model theory.

The notion of presentation in my understanding implies that what a given
presentation is a presentation *of* is somehow given in advance. I try to think
of a sketch as a means to build a theory, not to present a ready-made theory.
Perhaps *representation* is a better word for it than *presentation*.

best,
andrei