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Labeled posets are universal

Lehtonen, Erkko

European J. Combin., 29 (2008), 493-506

Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. The homomorphicity order of finite k-posets is shown to be a distributive lattice. Homomorphicity orders of finite k-posets and k-lattices are shown to be universal in the sense that every countable poset can be embedded into them. Labeled posets are represented by directed graphs, and a categorical isomorphism between k-posets and their digraph representations is established.