A $3$-poset is any of several concepts that generalize $2$-posets one step in higher category theory. One does not usually here about $3$-posets by themselves but instead as special cases of $3$-categories.

$3$-posets can also be called $(2,3)$-categories. The concept generalizes to $n$-posets.

Fix a meaning of $\infty$-category, however weak or strict you wish. Then a **$3$-poset** is an $\infty$-category such that all parallel pairs of $j$-morphisms are equivalent for $j \geq 3$. Thus, up to equivalence, there is no point in mentioning anything beyond $3$-morphisms, not even whether two given parallel $3$-morphisms are equivalent.

Last revised on March 12, 2009 at 02:02:09. See the history of this page for a list of all contributions to it.