Subject: categories: yetter&supernishimura

From: [email-masked] (Eduardo Dubuc)
Date: Tue, 19 Sep 2000 18:53:01 -0300 (ARG)

i quote from yetter's message:

"Does anyone have a full citation to the Nishimura paper which Dubuc
justly
criticizes for misattributing his construction?

I am interested because the title, and lack of care with citations,
suggest
the possibility that Nishimura is simply reproving results from my paper

D.N. Yetter, "Models for Synthetic Supergeometry", Cahier de Top. et Geom.
Diff. Cat. 29 (2) (1988) 87-108."

Nishimura's paper is titled "Supersmooth Topoi" (I have a only a preprint)

It is a  well referenced paper. In this paper Nishimura knows and
comments on Yetter's (1988). It is actually doing a different thing.

He uses my (with Taubin) construction with the notion of analytic ring
(1983), which is not to be found in [M-R] monograph. This notion is
algebraic but in the sense of a category with finite limits, not in the
sense of a category with finite products. (quotients are not suryective to
mention a difference)

just to clarify my letter, i quote again Yetter above:

"Dubuc justly criticizes for misattributing his construction?"

Well, Nishimura is using as a reference for my construction the
[M-R] monograph, and it is not at fault as I said. The problem is, that it
sounds ambigous because a whole situation I described in my letter

I quote now again from the [M-R] monograph two references concerning
specifically my work, which I found they  reveal a lot:

"Although this general notion of C-infinity
ring does not occur as such in classical analysis and differential
geometry, the main examples do ...  Given the role of these examples of
C-infinity rings in the classical literature, it is not surprising that
although the statements of several of the results in this chapter seem
new, most of their proofs are either known or easily derivable from known
ones".

"As far as terminology is concerned, we have
tried to avoid descriptions of the type "the Moerdijk envelop of the
Reyes topos", in favor of more informative ones"

well ...         eduardo dubuc