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Peter Johnstone Lectures: Some aspects of Topos Theory

Toposes as categories of manifolds

speaker: Peter Johnstone (University of Cambridge)

abstract: Among the toposes as categories of spaces, studied in Lecture 2, there are toposes which contain the classical category of smooth manifolds in a nice way. However, Lawvere observed that the higher-order structure of toposes can be used to give a remarkably simple "synthetic" axiomatization of differential geometry, in which differentiation becomes simply the operation of evaluation at an infinitesimal "disembodied tangent". To build toposes which are models for these axioms, one needs a little more than the category of manifolds; in this lecture we shall describe how models may be constructed using the algebraic theory of C-infinity rings.

timetable:
Tue 27 Apr, 14:30 - 16:30, Sala dei Seminari
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