  Assuming an abstract comparison principle called the Ultrapower Axiom, which
is motivated by the comparison process of inner model theory and generalizes
the statement that the Mitchell order is linear on normal ultrafilters, we
characterize strongly compact cardinals in terms of supercompactness: a
strongly compact cardinal is either supercompact or a limit of supercompact
cardinals. Assuming the Ultrapower Axiom and the GCH, we also prove a local
result that roughly states that every countably complete ultrafilter factors as
a finite iteration of supercompact ultrafilters.
