Cancelling coproducts?

Am I being dim here? In an extensive category (coproducts are preserved by pullbacks and are disjoint), can I cancel thus: X+1 ~= Y+1 ?=>? X ~= Y ? So far I have neither a proof nor a counterexample. If this cancellation principle exists it'll be slightly subtle, since 0+N ~= 1+N, and so we'd only be able to cancel adding a restricted class of (finite?) objects. I'd be grateful for either a proof or a counterexample! Michael Abbott 13-Nov-2002 13:41:53 -0400,662;000000000000-00000000