terminology: dagger and involution

[John Baez <baez@math.ucr.edu>]

On Thu, Mar 01, 2007 at 09:21:55AM +0000, V. Schmitt wrote:

> John Baez wrote:

> >by now there's enough literature using the term "dagger-categories"
> >that the genie is out of the bottle.

> Dear John, just my view: this is not a good argument.

It's not an argument - I'm just reporting on what I see.

I don't really like the term "dagger-categories", and I gently
tried to get people to stop using it, but it didn't work.  They're
already comfortable with it.

> I do not know about these dagger categories though
> i read about the compact closed ones.
> So may be I miss the point but, if this is the case, why
> introducing a new terminology if the concepts are not?
> That just creates confusion.

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!

Best,
jb