26 Feb
2007
26 Feb
'07
4:22 p.m.
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