Subject: categories: Re: terminology

From: Eduardo Dubuc <[email-masked]>
Date: Wed, 4 Jan 2006 11:59:15 -0300 (ART)

I have been asked why I reacted to the intended reeplacement of the names
"cartesian and cocartesian"  by  "prone and supine".  I have given several
reasons, but the one underlying the whole issue is the following:

The reason is that since a long time I have been worried about the ghetto
(in the sense of being isolated from the rest) characteristic of a certain
category theory community (or group of people). And P. May has reacted
concerning "prone and supine" probably because of reasons related to this.

The mathematical community  have been using "cartesian and cocartesian"
since always, and the introduction of "prone and supine" inside this
group will confirm even more the isolation. Examples abound, see M.Barr
introduction of "Molecular topos" to replace Grothendieck's "Locally
connected topos".

No matter how many linguistic points in favor a given name may have (like
prone and supine), to replace a well stablished  name intoduced by a
great mathematician (or school of mathematics) only puts you in
ridiculous.

P. May probably was feeling somehow that this will be extended by the
mathematical community to all category theory practicioners.

I profit by this mail to mention that concerning the concept "final" and
"initial", I am happy (and not surprised) to learn that these words have
been used since a long time to indicate the same categorical concept that
myself, and will certainly refer to the indicated bibliography to further
justify my use of these words.