|Cc:||andrei rodin <andrei@xxxxxxxxxxxxxxx>, "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>|
|From:||Alex Shkotin <alex.shkotin@xxxxxxxxx>|
|Date:||Tue, 8 Jul 2014 18:39:38 +0400|
just a few summer words about categories and Set theory.
1) Consider a very subtle category, may be a topos. Let's forget about composition for a moment - we get digraph.
Formal theory of digraphs itself is very interesting as it does not have an axioms at all.
We just need signature <Sorts ob, ar; Functions dom ar:ob, cod ar:ob>.
Well, we keep in mind that dom, cod are a full functions, but it's usual in math.
Unfortunately this important theory does not mentioned in great list
2) Goldblatt has mentioned somewhere in his book that we may look at ∈ as an arrow from element to set.
What Set theory does study then? Huge digraph:-)
It's more or less simple:
- there is no loops and cycles,
- there is no parallel arrows,
- there are sources (∅, pra-elements);
- there are sinks - classes;
But how many outcome arrows does have not a class? It's greater than any cardinal number.
2014-07-07 19:27 GMT+04:00 henson <henson.graves@xxxxxxxxxxx>:
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