Subject: categories: Re: Terminology again + Note from moderator

From: "Ronald Brown" <[email-masked]>
Date: Tue, 3 Jan 2006 12:21:59 -0000

Thanks to all who wrote on this - it has helped me to see the background and
issues in this important area for Categories for the Working Mathematician!

Ronnie

> [Note from moderator: This is to let you know that I am invoking the
> (not recently used) 48 hour rule for this subject: postings received
> by noon on Wednesday will be sent; after that the discussion may
> obviously continue, but not on the list.
> Best wishes to all for 2006, Bob Rosebrugh]

---

From: Toby Bartels <[email-masked]>
Date: Wed, 4 Jan 2006 02:59:41 -0800

jean benabou wrote in part:

>3.4- I can speak, read, and write a little bit of English, but I am
>French and might someday have the preposterous idea to lecture on
>fibered categories in French. Of course only in France, and to an
>audience uniquely composed of french persons. Perhaps MM Taylor and
>Johnstone, could suggest adequate french translations for prone and
>supine, which I can't seem to find. And they should be ready to do the
>same thing for German, Italian, Spanish, and many other languages.

>No such problems with cartesian of course, because cartesian.... is
>cartesian is cartesian is cartesian!

Jean B=E9nabou has three classes of arguments against "prone" and "supine":
ethical, mathematical, and linguistic.  The ethical argument
is particularly popular on this list, and the mathematical argument
(given in the post to which I'm replying) seems sound as well.
(But I hope that Paul Taylor or Peter Johnstone,
who used these words in print and sometimes read this list,
will reply, since they've probably thought about these matters too.)

However, I cannot accept the linguistic argument.
These words are not idiosyncratic, untranslatable English;
they are good Latin words with descendants in many languages.
It's true that they are both archaic or obsolete in French
(a loss for the world's francophones, I would say,
since they are useful words in any language),
but they have French forms that can be used.
Most of the other Romanic languages seem to have kept these words.

The Latin originals are (according to the Oxford English Dictionary)
"sup=EEn[us/a/um]" and "pr=F4n[us/a/um]" (where I use a cirumflex,
instead of the proper macron (TeX \=3D), to indicate a long vowel).
One can adapt these to any language that regularly borrows
from Latin (I'm afraid that I don't know how other languages
handle the Latin and pseudo-Latin that European mathematicians use).

I've also found the phrases "en supination" and "en pronation"
on francophone websites discussing sports medicine.
These are direct translations (at least for hands and feet)
of the English "supine" and "prone".  However, I don't think
that "morphisme en pronation" works as well as "morphisme prone",
even if the latter does resort to a 500-year-old word.

In Germanic languages (where compound neologisms are easier),
one might translate the meaning; a Google search suggests
that German words "bauchliegend" and "r=FCckenliegend"
have already been invented a few hundred times.

-- Toby