8 Oct
2007
8 Oct
'07
3:43 p.m.
(It helps to know ahead of time what answers are likely; fortunately there were no pure number theorists at my school.)
At the risk of sounding like a cracked record, how about the division category in lieu of the division lattice, namely the coproduct completion of the set P of primes as a discrete category? For a longer story use P* instead of P, P with a final object adjoined. Motivate the division category by pointing out that only the square-free positive integers can be recovered as sups of primes in the division lattice. Vaughan