Digital H-spaces and actions in the pointed digital homotopy category

We apply fundamental ideas from algebraic topology in mathematics to the digital world in computer science. We develop digital H-spaces and digital H-functions between the digital H-spaces with digital multiplications, and construct a necessary and sufficient condition for a digital H-space (or a digital homotopy associative H-space, a digital homotopy commutative H-space, or a digital H-group) to satisfy certain conditions in the category of magmas or a category of algebraic objects such as semigroups, monoids, or groups. We also investigate an action on the set of pointed digital homotopy (associative or commutative) multiplications to create new digital homotopy (resp., associative or commutative) multiplications.