nLab
3-poset

A 33-poset is any of several concepts that generalize 22-posets one step in higher category theory. One does not usually here about 33-posets by themselves but instead as special cases of 33-categories.

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

Definition

Fix a meaning of \infty-category, however weak or strict you wish. Then a 33-poset is an \infty-category such that all parallel pairs of jj-morphisms are equivalent for j3j \geq 3. Thus, up to equivalence, there is no point in mentioning anything beyond 33-morphisms, not even whether two given parallel 33-morphisms are equivalent.

Revised on March 12, 2009 02:02:09 by Toby Bartels (71.104.234.95)