[Haskell-cafe] Category Theory woes
Hans Aberg
haberg at math.su.se
Thu Feb 18 16:28:44 EST 2010
On 18 Feb 2010, at 22:06, Daniel Fischer wrote:
>>> ...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.
>
> Typo, iii. c(c(x)) = c(x), of course.
Sure.
> If we replace "set" by "lattice element" and "contains" by ">=", the
> definitions are equivalent.
Right.
> The one you quoted is better, though.
It is a powerful concept. I think of a function closure as what one
gets when adding all an expression binds to, though I'm not sure that
is why it is called a closure.
Hans
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