Re: terminology: dagger and involution

[Robert Seely <rags@math.mcgill.ca>]

On Thu, 1 Mar 2007, John Baez wrote:

> I hope this is clear: "dagger-categories" are completely different
> from "compact closed categories".  We need *some* term for them;
> we're just arguing about whether to call them "star-categories",
> "dagger-categories", or "categories with involution".  I like
> "star-categories", because in analysis and quantum topology the
> special case of "C*-categories" is very important.  But, I doubt
> we'll reach any sort of agreement!

You are completely right, of course - but one thing was clear from the
start: naming a structure from the notation used is rarely a smart
move; instead one should try to capture the essence of the structure
in the name.  (For that reason, "star-categories" isn't a whole lot
better than "dagger-categories", though admittedly, it's hard to think
of a worse name!  However, "star-categories" is likely to make folks
think "dagger = star", and that would be unhelpful.  That is probably
partially why getting a good name was tricky - after all, "dagger-
categories" sounds like the act of a desparate person failing to come
up with a good name.)

But by now, too many folks are probably unwilling to change (and there
isn't really an obvious better name anyway), and their collegues and
students will probably follow suit, making a name revision even less
likely.  Pity though ...

-= rags =-


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