  Generalizing the notion of a Koszul algebra, a graded k-algebra A is K2 if
its Yoneda algebra is generated as an algebra in cohomology degrees 1 and 2. We
prove a strong theorem about K2 factor algebras of Koszul algebras and use that
theorem to show the Stanley-Reisner face ring of a simplicial complex is K2
whenever the Alexander dual simplicial complex is (sequentially)
Cohen-Macaulay.
