| Summary: | In this paper, we consider the digital cohomology modules of a digital image consisting of a bounded and finite subset of <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">Z</mi><mi>n</mi></msup></semantics></math></inline-formula> and an adjacency relation. We construct a contravariant functor from the category of digital images and digital continuous functions to the category of unitary <i>R</i>-modules and <i>R</i>-module homomorphisms via the category of cochain complexes of <i>R</i>-modules and cochain maps, where <i>R</i> is a commutative ring with identity <inline-formula><math display="inline"><semantics><msub><mn>1</mn><mi>R</mi></msub></semantics></math></inline-formula>. We also examine the digital primitive cohomology classes based on digital images and find the relationship between <i>R</i>-module homomorphisms of digital cohomology modules induced by the digital convolutions and digital continuous functions.
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