Subject: categories: Upper case and lower case

From: Paul Taylor <[email-masked]>
Date: Mon, 13 Jul 1998 16:37:43 +0100 (BST)

> In mathematics many structures  are named after some one's name.

A questionable practice in many cases, and not necessarily complimentary
to the person concerned.  For example, G. H. Hardy is famous in genetics
for a rather trivial lemma in Bayesian statistics which was his answer
to a question over High Table lunch in Trinity one day.  How on earth is
anyone meant to know what might be meant by "Gauss's Lemma/Theorem/etc"?

On the other hand, things can be knocked off inappropriate pedestals by
giving them eponymous names.  For example, what others call "simple type
theory" or "higher order intuitionistic logic" I call "Zermelo type theory"
in my book.  This has certainly given me a more balanced view of its
(limited) importance in mathematics, and I hope to have the same effect
on my readers.

Given that you're doing it, whether to use a capital depends on national
and linguistic custom. The German phrase "hilbertische Raum" looks very
peculiar to me, for example.  I was brought up to give people capital
letters, whether they're nouns or adjectives.  I tend *not* to do this
if it seems to me that usage of the word has strayed rather a long way
from what the person in question actually did, for example "cartesian
transformation" for a natural transformation whose naturality squares
are pullbacks.

Peter Freyd, who of course comes from a different culture from me, will
probably tell you his views.

Paul

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From: James Stasheff <[email-masked]>
Date: Mon, 13 Jul 1998 16:34:30 -0400 (EDT)

and then there is the traditon of misassigning priority by nameing the
concept

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