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 wlawvere@acsu.buffalo.edu 106 Diefendorf Hall 716-829-2144 ext. 117 Buffalo, N.Y. 14214, USA **********************************************************************