John Baez wrote in part:
A dagger-category is a category C with a functor F: C -> C^{op} which is the identity on objects and has F^2 = 1.
Category theorists will note that the above definition is "evil", in the technical sense of that term: http://ncatlab.org/nlab/show/evil Namely, it imposes equations between objects, so we cannot transport a dagger-category structure along an equivalence of categories.
Often evil concepts (like the concept of "strict monoidal category") have non-evil counterparts (like the concept of "monoidal category"). But in this particular case I know no way to express the idea without equations between objects. Both Hilb and nCob are dagger-categories. This fact is important. Try saying it in a non-evil way!
By default, there is a non-evil way to say it: Given a category C, a _non-evil dagger-category structure_ on C consists of a dagger-category C' and an equivalence F: C -> C' of categories. So one question is whether there is a less long-winded way to say that. Another question (which logically comes before the first question) is what is the right notion of equivalence of such structures. --Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]