Attribution re no membership-respecting morphisms

Attribution re no membership-respecting morphisms

[Vaughan Pratt]

I've attributed the third saying at

   http://boole.stanford.edu/dotsigs.html

to Mike Barr.  If there's an earlier attribution I should be using
please let me know.

Vaughan Pratt

Re: Attribution re no membership-respecting morphisms

[Michael Barr]

Here is what the site actually says:

Monotone functions respect order, group homomorphisms respect the group
operation, linear transformations respect linear combinations, and
gangsters respect membership in the Cosa Nostra, but what morphism has
ever respected membership in a set? It is sheer hubris for a relation that
can't get no respect to claim to support all of mathematics.
(Old argument of category theorist Mike Barr, new polemics.)

That is not a bad rendition (save for the reference to Cosa Nostra) of
what I actually said which was that we create these elaborate structures
of well-founded trees subject to the rule that two chidren of the same
leaf cannot be isomorphic.  But then, unlike all other structures that we
build, we make no hypothesis that functions preserve the structure.
Indeed, I think a structure-preserving map must be the inclusion of a
subset.  And there are no non-identity endomorphisms.

On Mon, 21 Aug 2006, Vaughan Pratt wrote:

> I've attributed the third saying at
>
>    http://boole.stanford.edu/dotsigs.html
>
> to Mike Barr.  If there's an earlier attribution I should be using
> please let me know.
>
> Vaughan Pratt
>
>