  We present a unifying framework for the key concepts and results of higher
Koszul duality theory for N-homogeneous algebras: the Koszul complex, the
candidate for the space of syzygies, and the higher operations on the Yoneda
algebra. We give a universal description of the Koszul dual algebra under a new
algebraic structure. For that we introduce a general notion: Gr\"obner bases
for algebras over non-symmetric operads.
