Difference and Duality

[Venkata Rayudu Posina <posinavrayudu@gmail.com>]

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


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