A projective resolution of a unital R-module 
over a unit
ring 
is an exact sequence
 |
in which each 
is a projective module (Brown 1982). The projective dimension is the least length of
such a resolution, allowing infinity. Applying a covariant additive
functor from the category of unital
R-modules to an Abelian category to
a projective resolution provides a way to compute its left derived
functors. For example, 
is a projective resolution
over 
for every integer 
.
