[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* 
>     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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