Toposes as spaces
speaker: Peter Johnstone (University of Cambridge)abstract: Grothendieck's original insight was that a topos may be viewed as a generalized topological space. Many familiar properties of spaces and of continuous maps between them have natural generalizations to toposes and geometric morphisms (the analogue of continuous maps) between them. The interesting thing is that many properties which are commonly thought of as properties of spaces are really properties of continuous maps, applied to the unique map from the space to the 1-point space; expressing them in topos-theoretic terms thus allows us to "relativize" them, by considering geometric morphisms between arbitrary toposes having the same property. In this lecture we shall consider in particular the property of openness for continuous maps, and those of global and local connectedness for spaces; we shall also discuss local maps of toposes.
timetable:
Tue 13 Apr, 14:30 - 16:30, Sala Stemmi
<< Go back