nLab
1-poset

Fix a meaning of \infty-category, however weak or strict you wish. Then a 11-poset is an \infty-category such that every 22-morphism is an equivalence and all parallel pairs of jj-morphisms are equivalent for j1j \geq 1. Thus, up to equivalence, there is no point in mentioning anything beyond 11-morphisms, not even whether two given parallel 11-morphisms are equivalent. Up to equivalence, therefore, all that is left in this definition is a poset. Thus one may also say that a 11-poset is simply a poset.

The point of all this is simply to fill in the general concept of nn-poset; nobody thinks of 11-posets as a concept in their own right except simply as posets. Compare 11-category and 11-groupoid, which are defined on the same basis.

Revised on March 17, 2009 16:36:57 by Toby Bartels (71.104.234.95)