There is a natural cohomology theory for presheaves of algebras over small categories which governs their deformaton theory. The Cohomology Comparison Theorem asserts that this cohomology is identical to that of a single algebra constructed from the presheaf. This applies, in particular to equivariant cohomology where one has a group acting on an algebra, for a group is just a small category with a single object in which all the morphism are isomorphisms. Another very special case asserts that simplicial cohomology is a special case of Hochschild cohomology.