Re: Set as a monoidal category

[RONALD BROWN <ronnie.profbrown@btinternet.com>]

Dear Categoreans, 

It is standard practice to answer a different question! But I can't resist referring to 
R. Brown   ``Ten topologies for $X\times Y$'', {\em Quart. J.Math.}
(2) 14 (1963),  303-319.
and asking if one can modify these topologies or underlying sets by some process to work sensibly for the category of sets? (a compact subset of a discrete space is of course finite). Maybe it is not possible. 

Ronnie






----- Original Message ----
From: Peter Selinger <selinger@mathstat.dal.ca>
To: Categories List <categories@mta.ca>
Sent: Wednesday, 13 August, 2008 1:23:59 AM
Subject: categories: Set as a monoidal category

Dear Categoreans,

I know three monoidal structures on the category of sets, all of them
symmetric. Two are the product and coproduct, and I'll leave it to
your imagination to figure out the third one.

My question is: are these the only three? Proofs, counterexamples, or
references appreciated.

Thanks, -- Peter