terminology: dagger and involution

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

Marco wrote:

>what you are calling a "dagger-category", i.e.
>
>    a category equipped with a contravariant involutive
>    endofunctor, which is the identity on objects,
>
>has been called "a category with involution", at least from Burgin
>1969 to Lambek 2001. "Involutive category" has also been used, if
>less.
>
>I think it would be better to come back to the old term, which is
>meaningful, translatable, and old.

There's also a body of work, mainly from mathematical physics, that
calls these categories "star-categories".

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

Best,
jb