(infinity,0)-category

Following the terminology of (n,r)-categories, an **$(\infty,0)$-category** is an ∞-category in which every $j$-morphism (for $j \gt 0$) is invertible.

So in an $(\infty,0)$-category *every* morphism is invertible. Such ∞-categories are usually called *∞-groupoids*.

This is directly analogous to how a 0-category is equivalent to a set, a (1,0)-category is equivalent to a groupoid, and so on. (In general, an (n,0)-category is equivalent to an n-groupoid.)

The term “$(\infty,0)$-category” is rarely used, but does for instance serve the purpose of amplifying the generalization from Kan complexes, which are one model for ∞-groupoids, to quasi-categories, which are a model for (∞,1)-categories.

Revised on July 3, 2009 19:02:29
by Toby Bartels
(71.104.230.172)