homotopy hypothesis-theorem
delooping hypothesis-theorem
stabilization hypothesis-theorem
A 2-poset is any of several concepts that generalize (categorify) the notion of posets one step in higher category theory. One does not usually hear about -posets by themselves but instead as special cases of -categories, such as the locally posetal ones.
-posets can also be called (1,2)-categories, being a special case of (n,r)-categories. The concept generalizes to -posets.
A 2-poset is a category such that
is only a 2-proset if only satisfies 1-3.
Fix a meaning of -category, however weak or strict you wish. Then a -poset is an -category such that 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. This definition may give a concept more general than a locally posetal -category for your preferred definition of -category, but it will be equivalent if you ignore irrelevant data.
Just as the motivating example of a -category is the -category Cat of categories, so the motivating example of a -poset is the -poset Pos of posets.
2-poset
Last revised on September 19, 2022 at 20:00:32. See the history of this page for a list of all contributions to it.