Editing Order embedding (section)

== Additional perspectives ==
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Posets can straightforwardly be viewed from many perspectives, and order embeddings are basic enough that they tend to be visible from everywhere. For example:
* ([[Model theory|Model theoretically]]) ''A'' poset is a set equipped with a (reflexive, antisymmetric and transitive) [[binary relation]]. An order embedding ''A'' → ''B'' is an isomorphism from ''A'' to an [[elementary substructure]] of ''B''.
* ([[Graph theory|Graph theoretically]]) ''A'' poset is a (transitive, acyclic, directed, reflexive) [[Graph (discrete mathematics)|graph]]. An order embedding ''A'' → ''B'' is a [[graph isomorphism]] from ''A'' to an [[induced subgraph]] of ''B''.
* ([[Category theory|Category theoretically]]) A poset is a (small, thin, and skeletal) [[category (mathematics)|category]] such that each [[hom-set|homset]] has at most one element. An order embedding ''A'' → ''B'' is a full and faithful [[functor]] from ''A'' to ''B'' which is injective on objects, or equivalently an isomorphism from ''A'' to a [[full subcategory]] of ''B''.