Note that a sequence
of sheaves of abelian groups is exact if and only if it is exact stalkwise.
be an exact sequence of sheaves of abelian groups on a topological space . Then:
of sections is exact.
may not be surjective in general.
In a language of category theory, the global section function
is a left exact functior. (But not exact.) To treat it, we employ derived functors.
: injective injective for any .