Re: terminology: dagger and involution

[Marco Grandis <grandis@dima.unige.it>]

Dear John,

Sooner or later somebody will call them "sharp" categories, or
"tilde" categories...  What you are saying is a good argument in
favour of a sensible, well established name.

Also, on a more general ground, should we have a different
terminology in, say:

- category theory,
- category theory applied to computer science,
- category theory applied to physics?

Funny names, like quark, can be good and typographical names can be
useful, when there is no better substitute. Eg, I do not know of any
good substitute for "comma category". But I see no reason to replace
a sensible name with a meaningless one; or, even worse, many
meaningless ones.

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Dear Jeff,

The problem you are mentioning is essentially based on terminology
for different dualities in higher categories. I do not think there is
a way of finding a coherent terminology for them, which would not
clash with some well established, quite sensible use, already
existing in some particular case.
Therefore, I would not be surprised if the contravariancy of an
involution should assume different meanings in different contexts.

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All the best

Marco