# Article

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Keywords:
relations of type $\alpha$; reflexivity; diagonality; strong regularity; homomorphism; extended preorders
Summary:
There exists a natural extension of the notion of preorder from binary relations onto relations whose arities are arbitrary ordinals. In the article we find a condition under which extended preorders coincide with preorders if viewed categorically.
References:
[1] Y. Bar-Hillel A.A. Fraenkel A. Levy: Foundations of Set Theory. North Holland, Amsterdam, 1973. MR 0345816
[2] E. Čech: Topological papers of Eduard Čech, Ch. 8. Academia, Prague, 1968, pp. 436-472. MR 0248705
[3] H. Herrlich: Cartesian closed topological categories. Math. Coll. Univ. Cape Town 9 (1974), 1-16. MR 0460414 | Zbl 0318.18011
[4] S. Mac Lane: Categories for the Working Mathematician. Springer-Verlag, Heidelberg-New York, 1971. MR 0354798 | Zbl 0232.18001
[5] V. Novák: On a power of relational structures. Czech. Math. J. 35 (1985), 167-172. MR 0779345
[6] J. Šlapal: Relations of type $\alpha$. Zeitschr. f. math. Logik und Grundl. d. Math. 34 (1988), 563-573. DOI 10.1002/malq.19880340608 | MR 0973399
[7] J. Šlapal: Cartesian closedness in categories of relational systems. Arch. Math. (Basel) 52 (1989), 603-606. DOI 10.1007/BF01237574 | MR 1007636
[8] J. Šlapal: Relations and topologies. Czech. Math. J. 43 (1993), 141-150. MR 1205237

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