[Haskell-cafe] Category Theory woes

Gregg Reynolds dev at mobileink.com
Thu Feb 18 12:24:13 EST 2010

On Thu, Feb 18, 2010 at 7:48 AM, Nick Rudnick <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.

> * 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.

> 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.

> Categories: In every day's language, a category is a completely different
> thing, without the least

Not necesssarily (for Kantians, Aristoteleans?)  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.

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