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ternary semigroup; mono-n-ary structure; mono-n-ary algebra; category; homomorphism; strong homomorphism; isomorphism
In this paper the notion of a ternary semigroup of morphisms of objects in a category is introduced. The connection between an isomorphism of categories and an isomorphism of ternary semigroups of morphisms of suitable objects in these categories is considered. Finally, the results obtained for general categories are applied to the categories $\bold{ REL}n+1$ and $\bold {ALG}n$ which were studied in [5].
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