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Multimorphisms over enumerated sets

The concept of a multimorphism over enumerated sets is a natural generalization of the classical concept of a morphism of enumerated sets. Moreover, there are some connections between multimorphisms and binary relations over enumerated sets (Orlicki [3]). These connections are presented in the first part of the paper. In the second part the main results of the paper are given. The third part shows us that multimorphisms are not "exotic" — they appear in Recursion Theory.