Gregg Reynolds wrote:
On Thu, Feb 18, 2010 at 7:48 AM, Nick Rudnick
<joerg.rudn...@t-online.de <mailto: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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