6 July 2004

2:30 - 4:00     M. Barr
                Perfect maps of spaces

Abstract:
A perfect map is continuous, closed, and compact (inverse image of a
compact set is compact).  Let Perf be the category of Hausdorff spaces and
perfect maps.  Then Perf is not complete (lacks a terminal object) but has
all fibre products.  Moreover Perf is an exact category.  The result is
that for any space Z, the underlying functor Perf/Z --> Perf/|Z| is
tripleable.  Moreover, a perfect map Z --> Z' induces a functor
Perf/Z' --> Perf/Z (pullback) that has a left adjoint (composition) and is
itself tripleable iff Z --> Z' is (regular) epic.  (All epics are
surjective quotient mappings.)