The four lemma is a diagram lemma stating that, given the above commutative diagram whose rows are exact sequences, the following holds:
1. If 
is surjective,
and 
and 
are injective, then 
is injective;
2. If 
is injective,
and 
and 
are surjective, then 
is surjective.
This lemma is closely related to the five lemma, which is based on a similar diagram obtained by adding a single column.
