  In this paper we study the extent to which Golodness may be transferred along
morphisms of DG-algebras. In particular, we show that if $I$ is a so-called
fiber invariant ideal, then Golodness of $I$ is equivalent to Golodness of the
initial ideal of $I$. We use this to transfer Golodness results for monomial
ideals to more general classes of ideals. We also prove that any so-called
rainbow monomial ideal with linear resolution defines a Golod ring; this result
encompasses and generalizes many known Golodness results for classes of
monomial ideals. We then combine the techniques developed to give a concise
proof that maximal minors of (sparse) generic matrices define Golod rings,
independent of characteristic.
