Fix a meaning of -category, however weak or strict you wish. Then a -poset is an -category such that every -morphism is an equivalence and all parallel pairs of -morphisms are equivalent for . Thus, up to equivalence, there is no point in mentioning anything beyond -morphisms, not even whether two given parallel -morphisms are equivalent. Up to equivalence, therefore, all that is left in this definition is a poset. Thus one may also say that a -poset is simply a poset.
The point of all this is simply to fill in the general concept of -poset; nobody thinks of -posets as a concept in their own right except simply as posets. Compare -category and -groupoid, which are defined on the same basis.