My posting

My posting

[Michael Barr]

Oops!

I thank Peter J. for an extremely gentle explanation.  And yes, Peter F.,
I did once take note of a certain lack of elements in the empty set, but,
believe it or not that was not the real source of my error.  But that was
so unbelievably dumb that I will keep it secret. 

Michael

My posting

[Michael Barr]

>From Todd Wilson, I learned that adding identities is not so harmless.  
So suppose only that there are objects, arrows, source and target and
arrows that compose associatively only when source matches target.  With
identities, you can conclude, for any idempotent e, from eee = e1e, that e
= 1 and that makes it trivial.

Michael

My posting

[categories]

Date: Thu, 31 Jul 1997 21:33:58 -0400
From: Michael Barr <barr@triples.math.mcgill.ca>

I regret that my recent posting on Pratt's construction should not
have been sent to categories.  He sent me privately a construction
showing that A -o A has at least 2^K dinatural endomorphisms (that
is the diagonalization of the functor that takes A,B to A -o B) in
chu(Set,K) and I mistakenly thought it had come off the categories
bulletin board.  But it had been sent to me privately.  In any case, 
the claim is correct and my description for K = 2 is too.

Sorry for the mixup.

Michael