[Haskell-cafe] Category Theory woes
Nick Rudnick
joerg.rudnick at t-online.de
Thu Feb 18 13:55:31 EST 2010
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
>
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