  Under certain conditions, Koszul complexes can be used to calculate relative
Betti diagrams of vector space-valued functors indexed by a poset, without the
explicit computation of global minimal relative resolutions. In relative
homological algebra of such functors, free functors are replaced by an
arbitrary family of functors. Relative Betti diagrams encode the multiplicities
of these functors in minimal relative resolutions. In this article we provide
conditions under which grading the chosen family of functors leads to explicit
Koszul complexes whose homology dimensions are the relative Betti diagrams,
thus giving a scheme for the computation of these numerical descriptors.
