  In this paper, we extend constructions and results for the Taylor complex to
the generalized Taylor complex constructed by Herzog. We construct an explicit
DG-algebra structure on the generalized Taylor complex and extend a result of
Katth\"an on quotients of the Taylor complex by DG-ideals. We introduce a
generalization of the Scarf complex for families of monomial ideals, and show
that this complex is always a direct summand of the minimal free resolution of
the sum of these ideals. We also give an example of an ideal where the
generalized Scarf complex strictly contains the standard Scarf complex.
Moreover, we introduce the notion of quasitransverse monomial ideals, and prove
a list of results relating to Golodness, Koszul homology, and other homological
properties for such ideals.
