  For a certain full additive subcategory X of an additive category A, one
defines the lower extension groups in relative homological algebra. We show
that these groups are isomorphic to the suspended Hom groups in the Verdier
quotient category of the bounded homotopy category of A by that of X.
Alternatively, these groups are isomorphic to the negative cohomological groups
of the Hom complexes in the dg quotient category A/X, where both A and X are
viewed as dg categories concentrated in degree zero.
