Subject: categories: announcement of pre-prints

From: F W Lawvere <[email-masked]>
Date: Thu, 19 Nov 1998 22:49:16 -0500 (EST)

There are two items now available for downloading (PDF) from
my homepage

		http://www.acsu.buffalo.edu/~wlawvere/
They are:

     Volterra's functionals and the covariant cohesion of space

Abstract:
	Volterra's principle of passage from finiteness to infinity is far
less limited than a linearized construal of it might suggest;  I outline
in Section III a nonlinear version of the principle with the help of
category theory.  As necessary background I review in Section II some of
the mathematical developments of the period 1887-1913 in order to clarify
some more recent advances and controversies which I discuss in Section I.
Some relevant historical and current literature is discussed in relation
to the categorical analysis:  Volterra and Hadamard on the notion of
element, Fichera's critique of the relation between functional analysis
and continuum physics, and the recent Michor & Kriegl book published by
the AMS.

	Outline of Synthetic Differential Geometry

Abstract:
These rough notes were distributed to the geometry seminar at Buffalo
in February 1998, sketching the background of categorical dynamics in
anticipation of the April 1999 AMS Meeting in which there will be a
special session on related matters.  In particular, some of the results
stated in my September 1997 AMS talk in Montreal "Toposes of laws of
motion" are outlined, especially the relation of second order differential
equations to a.t.o.m's (amazingly tiny object models).  An additional
appendix has been added (November 1998) to these rough notes concerning
recent advances on these questions by Kock and Reyes.

	Toposes of laws of motion
will be added to the web page as soon as the transcript of the original
video is completed.

**********************************************************************
F. William Lawvere			Mathematics Dept. SUNY 
[email-masked]               106 Diefendorf Hall
716-829-2144  ext. 117		        Buffalo, N.Y. 14214, USA

**********************************************************************