  Let X be a smooth toric variety defined by the fan {\Sigma} . We consider
{\Sigma} as a finite set with topology and define a natural sheaf of graded
algebras A_{\Sigma} on {\Sigma} . The category of modules over A_{\Sigma} is
studied (together with other related categories). This leads to a certain
combinatorial Koszul duality equivalence. We describe the equivariant category
of coherent sheaves coh_{X,T} and a related (slightly bigger) equivariant
category O_{X,T}-mod in terms of sheaves of modules over the sheaf of algebras
A_{\Sigma} . Eventually (for a complete X ) the combinatorial Koszul duality is
interpreted in terms of the Serre functor on D^b(coh_{X,T})
