  It is known that, for $C$ an abelian category and $I$ small, the functor
category $C^I$ is again abelian; thus we can do homology in such categories,
and examine how it relates to homology in $C$ itself. However, there does not
seem to be any good reference collecting these ideas together. This article
seeks to fill the gap by showing that homology in $C^I$ behaves as one would
expect.
