Re: dagger and involution

Re: dagger and involution

[Zinovy Diskin]

On 3/2/07, Robert Seely <rags@math.mcgill.ca> wrote:
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> But by now, too many folks are probably unwilling to change (and there
> isn't really an obvious better name anyway), and their collegues and
> students will probably follow suit, making a name revision even less
> likely.  Pity though ...


synonyms (and even homonyms) are widely spread in natural languages simply
because they are convenient. In reasonable doses they could be useful in
math too. It would be worse if their use were implicit but if daggerists and
involutists know that they speak about the same thing, then why not?

I do not want to say that both terms are equally good, or equally bad...
what I'm trying to say is that so far we simply do not know. It will be seen
later whether the community will prefer one over the other, or will continue
to use both... Language is normally regulated by usage rather than by
directives. The current discussion is quite useful if it is about usage, but
I'm afraid that it would be less useful if it takes the modality of
prescribing one and proscribing the other.

--zd

Re: dagger and involution

[Dusko Pavlovic]

deciding whether the involution on a category should be written as a
dagger or as a star sounds to me a bit like deciding whether a
polynomial should be in x or in y. i worked with people who use the
dagger, and didnt work with people who use the star, but it would be
good if i could keep my options open.

but anyway, denoting the math structures by the typographic symbols used
in them sounds like an amusing idea. after a hundred years of progress
in creating new structures, and metafonting new symbols for them, we'll
probably be in possession of a fairly rich new language of hieroglyphs.

-- dusko


John Baez wrote:

> [snip]
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>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
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