[Haskell-cafe] Category Theory woes

[Daniel Fischer]

Am Freitag 19 Februar 2010 02:48:59 schrieb Nick Rudnick:
> Hi,
>
> wow, a topic specific response, at last... But I wish you would be more
> specific... ;-)
>
> >> A *referrer* (object) refers to a *referee* (object) by a *reference*
> >> (arrow).
> >
> > Doesn't work for me. Not in Ens (sets, maps), Grp (groups,
> > homomorphisms), Top (topological spaces, continuous mappings), Diff
> > (differential manifolds, smooth mappings), ... .
>
> Why not begin with SET and functions...

Sorry, too many Bourbakists in my ancestry, Ens == SET (french: ensemble).

>
> Every human has a certain age, so that there is a function, ageOf::
> Human-> Int, which can be regarded as a certain way of a reference
> relationship between Human and Int, in that by agoOf,

I fail to see a reference here. In particular, I don't see how the one 
object (set of humans) refers to the other object (set of integers).
I suppose the word reference doesn't mean the same for us.
For me, a reference is an alias (as in e.g. Java's reference types) or a 
mention/allusion/citation (as in e.g. "The first verse of this poem is a 
reference to Macbeth's famous monologue 'Is this a dagger ...'"), a couple 
of other things I can't now put into english words. None of which I deem 
similar to a function from one set to another.

>
> * Int reflects a certain aspect of Human,

Okay.

> and, on the other hand,
> * the structure of Human can be traced to Int.

I don't understand that.

>
> Please tell me the aspect you feel uneasy with, and please give me your
> opinion, whether (in case of accepting this) you would rather choose to
> consider Human as referrer and Int as referee of the opposite -- for I
> think this is a deep question.
>
> Thank you in advance,
>
>     Nick