In this paper, we consider the digital cohomology modules of a digital image consisting of a bounded and finite subset of Zn and an adjacency relation. We construct a contravariant functor from the category of digital images and digital continuous functions to the category of unitary R-modules and R-module homomorphisms via the category of cochain complexes of R-modules and cochain maps, where R is a commutative ring with identity 1R. We also examine the digital primitive cohomology classes based on digital images and find the relationship between R-module homomorphisms of digital cohomology modules induced by the digital convolutions and digital continuous functions.