Re: [Haskell-cafe] Category Theory woes

Gregg Reynolds wrote:

On Thu, Feb 18, 2010 at 7:48 AM, Nick Rudnick mailto:joerg.rudnick@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