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• CommentRowNumber1.
• CommentAuthorzskoda
• CommentTimeJan 4th 2012

I have created the entry recollement. Adjointness, cohesiveness etc. lovers should be interested.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJan 4th 2012
• (edited Jan 4th 2012)

notice that we have a (stubby) entry six operations

• CommentRowNumber3.
• CommentAuthorzskoda
• CommentTimeJan 4th 2012
• (edited Jan 4th 2012)

I made a mistake. It is not directly related sorry. Six operations are an issue about Grothendieck duality, not recollement.

When Grothendieck talks about the yoga of six operations than he means a heuristic meta-theory encompasing a variety of contexts, not the single axiomatic framework – it is a general story about the derived duality in mathematics. The recollement seems introduced by Beilinson-Bernstein-Deligne much later and is a much simpler issue.

• CommentRowNumber4.
• CommentAuthorMike Shulman
• CommentTimeMay 18th 2012

Why is the word “recollement” not translated into English? E.g. google translate suggests “reattachment” or “gluing”.

• CommentRowNumber5.
• CommentAuthorzskoda
• CommentTimeMay 18th 2012

I would prefer that it does stay so. Gluing is taken often as a synonym of a descent, while recollement is a more specific situation, and it is good that the term is referred to with a standard and technical term. Reattachement would be a better candidate as, unlike gluing, it is not used in math much so far, but so many English papers already use ”recollement”.

• CommentRowNumber6.
• CommentAuthorMike Shulman
• CommentTimeMay 19th 2012

How do English speakers pronounce it?

• CommentRowNumber7.
• CommentAuthorzskoda
• CommentTimeMay 19th 2012

What I hear is the same as in French, but without nasalization and with true n.

• CommentRowNumber8.
• CommentAuthorMike Shulman
• CommentTimeMay 20th 2012

Not being a French speaker myself, that doesn’t help me. (-:

• CommentRowNumber9.
• CommentAuthorzskoda
• CommentTimeMay 20th 2012

rəkɔlman vs. rəkɔlm$\tilde{a}$

• CommentRowNumber10.
• CommentAuthorTim_Porter
• CommentTimeMay 20th 2012

As a bilingual speaker (;-)), if I was saying it, it would correspond to a spelling of ’recolment’ i.e. more or less as in French but sounding the nt in ment.

• CommentRowNumber11.
• CommentAuthorzskoda
• CommentTimeMay 20th 2012
• (edited May 20th 2012)

I never heard the nt pronounciation so far in English language talks on the subject (the word comes pretty often in algebraic geometry talks). I just hear identical to French without nasalization. I do not know of the usages out of mathematics.

• CommentRowNumber12.
• CommentAuthorTim_Porter
• CommentTimeMay 20th 2012

You will have to get me to say it to you next time we meet! Often English speakers adopt a pseudo-French pronunciation and that is probably what you have heard.

• CommentRowNumber13.
• CommentAuthorzskoda
• CommentTimeMay 21st 2012

Right, so what is wrong with it ? It is still written French and sc ientists use the pseudo-French quite well, while in Schrift we can italicize those. Even on cuneiform tablets embedded foreign words used to be italicized in their graphics: Glossenkeil consisting of two Winkelhaken signs was used before a phrase quoted in another language. This witnessed that speakers of natural languages even in dawn of literacy were aware of embedding status and were comfortable with conventions of switching.

• CommentRowNumber14.
• CommentAuthorMike Shulman
• CommentTimeMay 29th 2012

FWIW, the analogous topos-theoretic context is almost always called (Artin) gluing, and I haven’t ever heard anyone complain about a clash between that sort of gluing and sheafy gluing.

• CommentRowNumber15.
• CommentAuthorzskoda
• CommentTimeMay 29th 2012

You say that I should learn what “FWIW” is, but I should not learn word recollement ?

• CommentRowNumber16.
• CommentAuthorMike Shulman
• CommentTimeMay 29th 2012

Well, FWIW is an abbreviation of an English phrase.

• CommentRowNumber17.
• CommentAuthorMike Shulman
• CommentTimeMay 29th 2012

Also, I would never use FWIW in a mathematical paper, much less as a mathematical definition.

• CommentRowNumber18.
• CommentAuthorzskoda
• CommentTimeMay 29th 2012
• (edited May 29th 2012)

But abbreaviations are not a part of natural (spoken) language, nor of standard orthography (apart from few like i.e.), they are the convention of limited communities which do not pretend to present the general language corpus. Look at wikipedia for D.M.V. for example, it denotes more than 10 different phrases. I know it as my former director needed to be called by D.M.V.

Strangely enough both communist SSSR and USA have big like for abbreviations, far more than German and especially far more than French, and I can say, certainly far more than Croatian. Dieudonne was once writing something about this while defending the terminology of Bourbaki. Russia now has shorthands for English phrases like terakt for terrorist act and so on; terrible damage to their language.

• CommentRowNumber19.
• CommentAuthorzskoda
• CommentTimeMay 29th 2012
• (edited May 29th 2012)

Mathematical expressions and notation tend to borrow from many languages and scripts. Logicians like Hebrew notation, to mention the most notable example. Russian took for example сайт (sajt, or if you prefer, sayt) for (Grothendieck) site, which is transferred hence via a phonetic/pronounced version, and it is now entirely standard. I am now suggesting it into Croatian math terminology, the same way, sajt.

• CommentRowNumber20.
• CommentAuthorMike Shulman
• CommentTimeMay 29th 2012

I’m not sure what your point is in #18.

I think it’s fine for mathematics to use different alphabets for symbols (there aren’t enough letters in one alphabet), but I don’t think it’s a good idea to use words from another language; they should be translated into the language in which you are writing. But “recollement” seems pretty well established even in English writing about these things, so probably it is not going to get changed.

• CommentRowNumber21.
• CommentAuthorzskoda
• CommentTimeMay 30th 2012

18 was just a comment illustrating that while you are absolutely right that FWIW may be understood as an abbreviation of an English phrase, it has likely not achieved a status of an abbreviation which is a part of the standard (general) English language sign, and that alleviating too many abbreviations to that status if it is going to happen would be of a debatable value.

• CommentRowNumber22.
• CommentAuthorUrs
• CommentTimeFeb 2nd 2016

I have cross-linked recollement and adjoint modality, and have added an Example-item at “recollement”: global equivariant stable homotopy theory.

(coming back to this four year old thread here: #15 is pretty funny)

• CommentRowNumber23.
• CommentAuthorjonrowlands
• CommentTimeJan 23rd 2019
• (edited Jan 23rd 2019)

The recollement page uses $j$ (resp. $i$) for the open (resp. closed) embedding, while Artin gluing uses the reverse. Is there a good way to reconcile them? I can make the edits if there’s agreement.

• CommentRowNumber24.
• CommentAuthorjonsterling
• CommentTimeJul 27th 2020
I believe SGA 4 uses j for the open embedding and i for the closed one as well... In case that helps.
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