We prove that two categories are isomorphic for any positive integer \(n\): Objects of the first category are \(n+1\)-ary relational structures where an \(n+1\)-ary relational structure is a set with one \(n+1\)-ary relation; morphisms of this category are strong homomorphisms of those structures. Objects of the second category are \(n\)-ary algebras where an \(n\)-ary algebra is a power set with a totally additive \(n\)-ary operation; morphisms of this category are totally additive atom-preserving homomorphisms of those algebras. This result generalizes the main theorem of the author’s earlier papers [ibid. 41, No. 1, 90-98 (1991; Zbl 0790.20090); ibid. 41, No. 2, 300-311 (1991; Zbl 0735.08005)], which represent particular cases of our present result for \(n=1\) and \(n=2\). Definitions presented in these papers for particular cases are now generalized. The proof of our theorem is omitted because it is almost the same as in the first paper quoted.