Geodesic
A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 213-221

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MR Zbl
We characterize totally ordered sets within the class of all ordered sets containing at least four-element chains. We use a simple relationship between their isotone transformations and the so called 1-endomorphism which is introduced in the paper. Later we describe 1-, 2-, 3-, 4-homomorphisms of ordered sets in the language of super strong mappings.
We characterize totally ordered sets within the class of all ordered sets containing at least four-element chains. We use a simple relationship between their isotone transformations and the so called 1-endomorphism which is introduced in the paper. Later we describe 1-, 2-, 3-, 4-homomorphisms of ordered sets in the language of super strong mappings.
Classification : 06A05, 06A06, 06A10, 06A99
Keywords: ordered sets; morphisms 
Halaš, Radomír; Hort, Daniel. A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 213-221. http://geodesic.mathdoc.fr/item/CMJ_2003_53_1_a16/
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