In mathematics, the Ext functors of homological algebra are derived functors of Hom functors. They were first used in algebraic topology, but are common in many areas of mathematics.
More precisely, write 
for the category of module over R, a ring. Let A be in 
and set 
, for fixed B in . (This is a left exact functor (contravariant) so we want its right derived functors RnT). To this end, define
i.e., take a projective resolution
compute
and take the cohomology on the righthand side.