Conceptual Mathematics question

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?

http://conceptualmathematics.wordpres...

F. William Lawvere