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poset; directed poset; semilattice; chain; monotone; strictly monotone; upper cone preserving; strictly upper cone preserving; strongly upper cone preserving; ordinal sum; induced equivalence relation

References:

[1] Berrone, L. R.: **The homomorphism equation on semilattices**. Aequationes Math. 94 (2020), 803-816. DOI 10.1007/s00010-020-00699-1 | MR 4145720 | Zbl 1448.39038

[2] Chajda, I.: **Homomorphisms of directed posets**. Asian-Eur. J. Math. 1 (2008), 45-51. DOI 10.1142/S1793557108000059 | MR 2400299 | Zbl 1159.06002

[3] Chajda, I., Goldstern, M., Länger, H.: **A note on homomorphisms between products of algebras**. Algebra Universalis 79 (2018), Paper No. 25, 7 pages. DOI 10.1007/s00012-018-0517-9 | MR 3788204 | Zbl 6904410

[4] Chajda, I., Hošková, Š.: **A characterization of cone preserving mappings of quasiordered sets**. Miskolc Math. Notes 6 (2005), 147-152. DOI 10.18514/MMN.2005.107 | MR 2199159 | Zbl 1095.08001