Dear All, There is a contrast between a map with a section and a map with a retract: in the case of a map with a section we can find proof [of belonging]; and in the case of a map with a retract we find that there is one proof. The contrast appears a little more pronounced: in trying to show that there is one proof f of h in r in the case of a map r with a section s, the closest I got is srf1 = srf2; and in trying to find proof of 'h is in s' in the case of a map s with a retract r, the closest I got is srh. Is there a duality (knowing answer vs. knowing that there is one answer) in here? Please forgive me for rushing to ask for help if this is something that can become clear as I go through 'The contravariant parts functor' article (I'm still on the first page of the article in Conceptual Mathematics). Thank you, posina [For admin and other information see: http://www.mta.ca/~cat-dist/ ]