Geodesic
Congruences in ordered sets and LU compatible equivalences
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 48 (2009) no. 1, pp. 153-156.

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A concept of equivalence preserving upper and lower bounds in a poset $P$ is introduced. If $P$ is a lattice, this concept coincides with the notion of lattice congruence.
Classification : 06A06, 06B10
Keywords: Ordered set; morphism; $LU$ compatible equivalence 
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Snášel, Václav; Jukl, Marek. Congruences in ordered sets and LU compatible equivalences. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 48 (2009) no. 1, pp. 153-156. http://geodesic.mathdoc.fr/item/AUPO_2009__48_1_a12/