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it had annoyed me for a long time that we had now dedicated entry for Giraud theorem. I have now created one, so that the redirects no longer simply go to Grothendieck topos. But then, I didn’t have the energy to add more than a few pointers, for the moment.
It has annoyed me that the entry for Jean Giraud hardly mentioned that theorem! It does now.
On a question of style and grammar (perhaps): should we write Giraud theorem as a title or Giraud’s theorem?
(I corrected ’a theorem of Giraud’s’ which seemed to me to be a double ’genitive’ case!:-)
okay, I have changed the title to Giraud’s theorem.
But since the entry is (mainly or also, depending on how it develops) a list of pointers to higher analogs, I think Giraud theorem is fine, too. “We have a Giraud theorem for $(n,r)$-toposes.” But we don’t have “Giraud’s theorem for $(n,r)$-toposes”, since he didn’t prove that except for the case $n = 1$, $r = 1$.
I corrected ’a theorem of Giraud’s’ which seemed to me to be a double ’genitive’ case!:-)
That’s not unheard of, of course – “a theorem of mine” is perfectly acceptable. :-) But I too prefer “theorem of Giraud”.
Warning: the cache bug currently infests Urs’s first link to Giraud theorem above.
I wonder if this is a case of constructions being different in other languages
I don’t think this is just me being German. Or is it? I continue to think what I said in #3: as soon as we pass beyond the particular statement that can be attributed to Giraud himself, we cannot speak of his theorem anymore, but we can still honor him and give his name to the type of theorem obtained this way.
This is common use (also among native English speaking authors, as far as I can see). For instance we find
Borceux’s standard textbook on category theory speaks of “Giraud theorem” here
the Encyclopedic dictionary of mathematics agrees with this, here
The “relative Giraud theorem” is always called this way, for instance here;
Mike introduced, it seems, the term “2-Giraud theorem” here. He also speaks of “Giraud theorem” here and elsewhere. If anyone, he should know.
Enrico Vitale’s thesis was titled “Giraud theorem” here (admittedly, he is not native English speaking)
Googling around, I find that there are “Giraud theorems” in other areas of math and also in other areas of science
There is also the Zaremba-Giraud theorem etc. pp. Ask Google if you don’t believe me.
Here is my two pennyworth!
On purely English stylistic grounds, I think that ’the Giraud theorem’ is fine, provided the context is clear and Giraud only proved one major result in that context. ‘The theorem of Giraud’ is not specific about which theorem of Giraud so will usually be followed with something like ’characterising Grothendieck toposes in terms of ….’. Jim’s suggestion of ’Giraud’s theorem’ (without the definite article) is perhaps somewhere between the two in meaning. In written material I think ’ a theorem of Giraud’ or ’the …’ is better than ’a theorem of Giraud’s’ which somehow might be said aloud, but is not standard written usage, at least in UK English. However I am fairly certain that ’the Giraud’s theorem’ is ’incorrect’.
NB These are my opinions and reflect the style I would probably use myself, but the important thing to avoid is a very ’heavy’ phraseology, and any ambiguity. I am wary of ’correct’ and ’incorrect’ as some sort of absolutes although I used ’incorrect’ a few lines back.
On a related but distinct topic, yesterday when looking for material on Giraud, I noticed that Google searches turned up another Jean Giraud with a mathematical connection. The BD (that is ’comic’) artist Jean Giraud whose ’nom de plume’ was Mobius has died at the age of 73. I have not found out why he took the name Mobius.
I have an impression —but without any comprehensive survey to back it up— that writing in English is moving from ‘X’s theorem’ to ‘the X theorem’. Grammatically, anything involving the English possessive case is very rigid, and if you’re going to manipulate words and names as we do in mathematics, it’s probably best to avoid the possessive as much as possible. (In German, you can write things like ‘der Satz eines Matematikers’, ‘ein Satz des Matematikers’, etc, which you just can’t do in English unless you abandon the possessive case for ‘of’. Speaking of which …)
On ‘a theorem of Giraud’s’, this is an interesting case where English has a distinction between animate and inanimate. The reason for this construction is the difference between ‘a picture of Giraud’s’ (in which Giraud is animate, being the person who made the picture) and ‘a picture of Giraud’ (in which Giraud is inanimate, being the object depicted in the picture). In cases where no confusion is possible, ‘a theorem of Giraud’s’ is more consistent, is the older usage, and is usually acceptable, but formal writing today prefers ‘a theorem of Giraud’ instead. With pronouns, however, the older usage prevails; it’s always ‘a theorem of mine’ and never ‘a theorem of me’. This construction is allowed only with persons, however; so in particular you should never see ‘of its’ (at the end of a phrase).
Interesting thoughts and excellent examples. :-) If you are right ‘a picture of Giraud’s’ is synonymous with ‘a picture amongst Giraud’s pictures’. It is the unspoken words that provide the grammatical structure, of course. Anyway we are probably getting ’off thread’. I think the main point should be ’does it feel ok!’ And it does to me.
If anyone, he should know.
Totally not true. (-:
Jim, Tim,
unless I am missing something, the wrong versions that you listed don’t appear here nor in any $n$Lab entry. Nor did they before.
Or maybe I am missing something. If there is wrong grammar on the $n$Lab, please say where.
There is a slight problem that when, for instance, we have Goursat theorem, it really does need ’the’ but that would muck up a lot of the rest of the conventions etc so is not important. The grammar looks fine in general. I started this discussion because I felt that ’the theorem of Giraud’s’ was awkward (not necessarily ungrammatical) and that the version without the ’s was less so. There are many very awkward wordings that do occur in many published papers. Some are so awkward that they obscure the meaning that is intended, but nothing of that scale occurs in the pages of the Lab as far as I know. (If there is an obscurity it usually gets ironed out quite quickly.)
In English at least, people usually leave ‘the’ out of titles, which I did when creating Goursat theorem, but there should be ‘the’ everywhere else. (Well, a couple of time I wrote ‘Goursat’s Theorem’, and I didn’t think very much about capital letters.)
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