Subject: categories: Terminology

From: jean benabou <[email-masked]>
Date: Sat, 10 Dec 2005 04:51:20 +0100

I have seen in this mail that the suggestion of Taylor and Johnstone to
replace cartesian and cocartesian maps by prone and supine ones begins to
be accepted. When I first saw that suggestion, I was so amazed that I
thought it was a joke, and not such a good one. I still hope it is no more
than that. But, just in case, and before it is too late, I want to say
that I am very strongly opposed to such changes for many reasons:
linguistic, mathematical, and ethical, which I am ready to explain in
detail if I am asked to do so.

---

From: Eduardo Dubuc <[email-masked]>
Date: Wed, 21 Dec 2005 17:04:11 -0300 (ART)

I very strongly agree with J. Benabou's comments about "prone" and
"supine", and P. May's opinion that "I'd like category theory no longer to
be regarded as nonsense in this country --- it still is in many quarters,
as I could easily prove --- and such terminology is not exactly helpful to
the cause!"

I recall P. Johnstone that he himself named his book  "Elephant Book"
because every body has different version of what a topos is, reflecting
only one of the many aspects of the concept.

Names like "Prone" and "Supine" correspond (with luck) to only one of the
many aspects of the concept of cartesian and its dual (in a sense)
cocartesian.

Also, there is a clear ethical aspect involved when a stablished
terminology that has been historically introduced by particular people
suffers a move to be eliminated and reeplaced by another.

But, coming back to the question above, i am also against the habit to
name a new mathematical concept with words that have a precise meaning in
everyday language (as prone, supine, etc).

Presisely, I do not know what does it mean exactly "Cartesian" (has
something to do with Descartes ...), but I know presisely what it is a
"Cartesian arrow" (in mathematics).

Colorful terminology taken from everyday language is an strong indication
to serious mathematicians that the subject should no be taken seriously
(see for example the claims of  "Catastrofe Theory" as opposed to the
sober "Classification of singularities of C-\infty mappings", and a lot of
similar examples).

As P May points out, "  . . .  such terminology is not exactly helpful to
the cause!".

The meaning of a mathematical concept should be given by the concept
itself, and not by the connotation that its name has in everyday language.

---

From: Vaughan Pratt <[email-masked]>
Date: Mon, 26 Dec 2005 11:47:32 -0800

Without taking sides on the prone/supine terminology question, I do have
a strong reaction to the Benabou/May/Dubuc concern that respect for a
field is undermined by its adoption of frivolous terminology.

This may be a valid concern for a young field like category theory, but
for a more mature subject such as physics, a more relevant concern is
the undermining of the ability to poke fun at oneself by the fear of not
being taken seriously.

Has the adoption of frivolous nomenclature for quarks ("strange,"
"charm," "beauty" and even "quark" itself) diminished in any way the
world's respect for quarks and their investigators?

And what of computational topology?  Should we turn a blind eye to
whether Scott is sober, and substitute a more genteel euphemism for his
bottom?

Vaughan Pratt

---

From: Eduardo Dubuc <[email-masked]>
Date: Thu, 29 Dec 2005 20:17:36 -0300 (ART)

We should not put everything in the same bag !!

"strange," "charm," "beauty" and even "quark" itself

are beautiful  and poetic names  to refer to objects or concepts which
precisely we do not want to associate any precise meaning in everyday
language, and on the other hand, the objects or concepts are  introduced
whith those names.

"prone/supine"  are all the contrary, they intent to reflect in everyday
language just one aspect of an existing concept which has many, and more
important, they are used in place of a well stablished name.

all this has nothing to do with  "young field" as opposed to "mature
subject"

silly names (if any) in physics would be as bad as in any other subject

do not confuse  things, I found  the  "Scott is sober" an exelent example
of humor that does not undermine respect for the field. Another exelent
example that comes to my mind is M. Barr's "The point of the empty set"

edubuc