1-1 Function, Category, Category of Sets, Category Theory, Codomain, Concept, Conceptual Mathematics, Domain, Element, Function, Inclusion, Logic, Map, Math, Monomorphism, Object, Part, Science, Set, Set Theory, Shape, Subobject, Theory, Truth
PART respects differences.
From → Note to self
Difference and Duality
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).
For admin and other information see: http://www.mta.ca/~cat-dist/
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!
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