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Ternary semigroups of morphisms of objects in categories

Antoni Chronowski, Miroslav Novotný (1995)

Archivum Mathematicum

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 $𝐑𝐄𝐋 n + 1$ and $𝐀𝐋𝐆 n$ which were studied in [5].

Ternary structures and groupoids

Miroslav Novotný (1991)

Czechoslovak Mathematical Journal

Ternary structures and partial semigroups

Vítězslav Novák (1996)

Czechoslovak Mathematical Journal

The algebraic uniqueness of the addition of natural numbers.

Elemer E. Rosinger (1982)

Aequationes mathematicae

The Słupecki criterion by duality

Eszter K. Horváth (2001)

Discussiones Mathematicae - General Algebra and Applications

A method is presented for proving primality and functional completeness theorems, which makes use of the operation-relation duality. By the result of Sierpiński, we have to investigate relations generated by the two-element subsets of $A^{k}$ only. We show how the method applies for proving Słupecki’s classical theorem by generating diagonal relations from each pair of k-tuples.