----- Forwarded Message -----
From: "Michael Matsko" <msmat...@comcast.net>
To: "Nick Rudnick" <joerg.rudn...@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.rudn...@t-online.de>
To: "Gregg Reynolds" <d...@mobileink.com>
Cc: "Haskell Café List" <haskell-cafe@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.rudn...@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
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