Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
ternary semigroup; mono-n-ary structure; mono-n-ary algebra; category; homomorphism; strong homomorphism; isomorphism
ternary semigroup; mono-n-ary structure; mono-n-ary algebra; category; homomorphism; strong homomorphism; isomorphism
Summary:
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].
References:
[1] MacLane S.: Categories for the working mathematician. Springer, New York - Heidelberg - Berlin 1971. MR 0354798
[2] Monk D., Sioson F. M.: m-Semigroups, semigroups, and function representation. Fund. Math. 59 (1966), 233-241. MR 0206133
[3] Novotný M.: Construction of all strong homomorphisms of binary structures. Czech. Math. J. 41 (116) (1991), 300-311. MR 1105447
[4] Novotný M.: Ternary structures and groupoids. Czech. Math. J. 41 (116) (1991), 90-98. MR 1087627
[5] Novotný M.: On some correspondences between relational structures and algebras. Czech. Math. J. 43 (118) (1993), 643-647. MR 1258426
[6] Novotný M.: Construction of all homomorphisms of groupoids. presented to Czech. Math. J.
[7] Pultr A., Trnková V.: Combinatorial, algebraic and topological representations of groups, semigroups and categories. Academia, Prague 1980. MR 0563525
[8] Sioson F. M.: Ideal theory in ternary semigroups. Math. Japon. 10 (1965), 63-84. MR 0193043 | Zbl 0247.20085
Search
Partner of
