  Extending constructions by Gabriel and Zisman, we develop a functorial
framework for the cohomology and homology of simplicial sets with very general
coefficient systems given by functors on simplex categories into abelian
categories. Furthermore we construct Leray type spectral sequences for any map
of simplicial sets. We also show that these constructions generalise and unify
the various existing versions of cohomology and homology of small categories
and as a bonus provide new insight into their functoriality.
