Homology and cohomology of cubical sets with coefficients in systems of objects

Abstract

This paper continues the research of the author on the homology of cubical and semi-cubical sets with coefficients in systems. The main result is the theorem that the homology of cubical sets with coefficients in contravariant systems in an Abelian category with exact coproducts is isomorphic to the left satellites of a colimit functor. It allowed proving a number of new assertions presented in this paper about homology and cohomology of cubical sets with coefficients in systems, including homology and cohomology with coefficients in local systems.