We introduce Cayley posets as posets arising naturally from pairs \(S<T\) of semigroups, much in the same way that a Cayley graph arises from a (semi)group and a subset. We show that Cayley posets are a common generalization of several known classes of posets, e.g., posets of numerical semigroups (with torsion) and more generally affine semigroups. Furthermore, we give Sabidussi-type characterizations for Cayley posets and for several subclasses in terms of their endomorphism monoid. We show that large classes of posets are Cayley posets, e.g., series–parallel posets and (generalizations of) join-semilattices, but also provide examples of posets which cannot be represented this way. Finally, we characterize (locally finite) auto-equivalent posets (with a finite number of atoms)—a class that generalizes a recently introduced notion for affine semigroups—as those posets coming from a finitely generated submonoid of an abelian group.

我们将Cayley姿势介绍为自然产生于\（S <T \）对的姿势半群，与以（半）群和一个子集产生Cayley图的方式几乎相同。我们证明，Cayley姿势集是几种已知类别的姿势集的通用概括，例如，数值半群（带有扭转）和更一般的仿射半群的姿势。此外，我们就Cayley球型和几个亚类的内同构体半身像给出了Sabidussi型特征。我们表明，大类的姿势是Cayley姿势，例如，串联-平行姿势和（联接）语义的一般化，但也提供了不能用这种方式表示的姿势的示例。最后，