Fwd: [Haskell-cafe] Category Theory woes
Nick Rudnick
joerg.rudnick at t-online.de
Thu Feb 18 15:15:49 EST 2010
Hi Mike,
so an open set does not contain elements constituting a border/boundary
of it, does it?
But a closed set does, doesn't it?
Cheers,
Nick
Michael Matsko wrote:
>
> ----- Forwarded Message -----
> From: "Michael Matsko" <msmatsko at comcast.net>
> To: "Nick Rudnick" <joerg.rudnick at t-online.de>
> Sent: Thursday, February 18, 2010 2:16:18 PM GMT -05:00 US/Canada Eastern
> Subject: Re: [Haskell-cafe] Category Theory woes
>
> Gregg,
>
>
>
> Topologically speaking, the border of an open set is called the
> boundary of the set. The boundary is defined as the closure of the
> set minus the set itself. As an example consider the open interval
> (0,1) on the real line. The closure of the set is [0,1], the closed
> interval on 0, 1. The boundary would be the points 0 and 1.
>
>
>
> Mike Matsko
>
>
> ----- Original Message -----
> From: "Nick Rudnick" <joerg.rudnick at t-online.de>
> To: "Gregg Reynolds" <dev at mobileink.com>
> Cc: "Haskell Café List" <haskell-cafe at haskell.org>
> Sent: Thursday, February 18, 2010 1:55:31 PM GMT -05:00 US/Canada Eastern
> Subject: Re: [Haskell-cafe] Category Theory woes
>
> Gregg Reynolds wrote:
>
> On Thu, Feb 18, 2010 at 7:48 AM, Nick Rudnick
> <joerg.rudnick at t-online.de <mailto:joerg.rudnick at t-online.de>> wrote:
>
> IM(H??)O, a really introductive book on category theory still
> is to be written -- if category theory is really that
> fundamental (what I believe, due to its lifting of
> restrictions usually implicit at 'orthodox maths'), than it
> should find a reflection in our every day's common sense,
> shouldn't it?
>
>
> Goldblatt works for me.
>
> Accidentially, I have Goldblatt here, although I didn't read it before
> -- you agree with me it's far away from every day's common sense, even
> for a hobby coder?? I mean, this is not «Head first categories», is
> it? ;-)) With «every day's common sense» I did not mean «a
> mathematician's every day's common sense», but that of, e.g., a
> housewife or a child...
>
> But I have became curious now for Goldblatt...
>
>
>
>
> * the definition of open/closed sets in topology with the
> boundary elements of a closed set to considerable extent
> regardable as facing to an «outside» (so that reversing these
> terms could even appear more intuitive, or «bordered» instead
> of closed and «unbordered» instead of open),
>
>
> Both have a border, just in different places.
>
> Which elements form the border of an open set??
>
>
>
> As an example, let's play a little:
>
> Arrows: Arrows are more fundamental than objects, in fact,
> categories may be defined with arrows only. Although I like
> the term arrow (more than 'morphism'), I intuitively would
> find the term «reference» less contradictive with the actual
> intention, as this term
>
> Arrows don't refer.
>
> A *referrer* (object) refers to a *referee* (object) by a *reference*
> (arrow).
>
>
>
> Categories: In every day's language, a category is a
> completely different thing, without the least
>
>
> Not necesssarily (for Kantians, Aristoteleans?)
>
> Are you sure...?? See
> http://en.wikipedia.org/wiki/Categories_(Aristotle) ...
>
> If memory serves, MacLane says somewhere that he and Eilenberg
> picked the term "category" as an explicit play on the same term in
> philosophy.
>
> In general I find mathematical terminology well-chosen and
> revealing, if one takes the trouble to do a little digging. If
> you want to know what terminological chaos really looks like try
> linguistics.
>
> ;-) For linguistics, granted... In regard of «a little digging», don't
> you think terminology work takes a great share, especially at
> interdisciplinary efforts? Wouldn't it be great to be able to drop,
> say 20% or even more, of such efforts and be able to progress more
> fluidly ?
>
>
> -g
>
>
>
> _______________________________________________ Haskell-Cafe mailing
> list Haskell-Cafe at haskell.org
> http://www.haskell.org/mailman/listinfo/haskell-cafe
> ------------------------------------------------------------------------
>
> _______________________________________________
> Haskell-Cafe mailing list
> Haskell-Cafe at haskell.org
> http://www.haskell.org/mailman/listinfo/haskell-cafe
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://www.haskell.org/pipermail/haskell-cafe/attachments/20100218/1526923c/attachment.html
More information about the Haskell-Cafe
mailing list