Short five lemma
In
mathematics, especially
homological algebra and other applications of
Abelian category theory, the
short five lemma is a special case of the
five lemma.
It states that for the following
commutative diagram (in any Abelian category), if the rows are
exact, and if
g and
h are isomorphisms, then
f is an isomorphism as well.
It follows immediately from the five lemma.