Given a short exact sequence of modules
 |
(1)
|
let
 |
(2)
|
 |
(3)
|
be projective resolutions of 
and 
, respectively. Then there is a projective resolution of 
 |
(4)
|
such that the above diagrams are commutative. Here, 
is the injection of the first summand, whereas 
is the projection onto the second
factor for 
.
The name of this lemma derives from the shape of the diagram formed by the short exact sequence and the given projective resolutions.
