Re: Bourbaki and Categories

[Andre.Rodin@ens.fr]

Of course, you are right about a point, I missed it! I must confess I didn't
think about this example in precise terms. My claim is that sketch theory
doesn't fit the structuralist (Bourbaki-Hilbertian) pattern. It hardly
precisely fits the ancient Euclidean pattern either but there is a suggestive
analogy, which concerns the idea that certain basic objects like point, line
and circle *generate* the rest.
A further claim is this: a specific reason *why* sketch theory doesn't fit the
structuralist pattern is that in sketch theory (like in CT in general)
isomorphisms don't have the same distinguished status.

andrei





>I don't know what to say about the suggestion that a circle and a line
>make a sketch of which Euclidean plane geometry is a model.  I would think
>you would need a point too, since intersections are crucial.  Maybe
>complex projective geometry since then two lines intersect in one point
>(unless they coincide), a line and a circle in two (unless they are
>tangent or equal) and every pair of circles in four (ditto).  Maybe the
>exceptions could be handled in some sketch.  At any rate, it wold e
>interesting to try to sketch this in detail.  At any rate, I never thought
>about this before.

>Michael