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).

You actually make it appear so easy together with your presentation however I find this matter to be really something which I think I’d by no means understand. It kind of feels too complicated and very wide for me. I am having a look ahead for your subsequent submit, I’ll try to get the cling of it!

Difference and Duality

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

fofhinrin the case of a maprwith a sections, the closest I got issrf1 =srf2; and in trying to find proof of ‘his ins‘ in the case of a mapswith a retractr, the closest I got issrh.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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You actually make it appear so easy together with your presentation however I find this matter to be really something which I think I’d by no means understand. It kind of feels too complicated and very wide for me. I am having a look ahead for your subsequent submit, I’ll try to get the cling of it!