Joyal Abstracts

Peter Johnstone

Where is the Elephant Going?

The publication of the first two volumes of "Sketches of an Elephant: a Topos Theory Compendium" is an appropriate moment to survey what we have learned about toposes over the past thirty years or so. This talk will attempt to describe some of the major achievements of topos theory (particularly those in which Andre Joyal has played a major part) and to suggest some future targets.