[Haskell-cafe] Category Theory woes
Hans Aberg
haberg at math.su.se
Thu Feb 18 15:47:02 EST 2010
On 18 Feb 2010, at 20:20, Daniel Fischer wrote:
>> + definition backtracking: «A closure operation c is defined by the
>> property c(c(x)) = c(x).
>
> Actually, that's incomplete, ...
That's right, it is just the idempotency relation.
> ...missing are
> - c(x) contains x
> - c(x) is minimal among the sets containing x with y = c(y).
It suffices*) with a lattice L with relation <= (inclusion in the case
of sets) satifying
i. x <= y implies c(x) <= c(y)
ii. x <= c(x) for all x in L.
iii. c(c(x)) = x.
Hans
*) The definition in a book on lattice theory by Balbes & Dwinger.
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