(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 an equivalence.

So in an $(\infty,0)$-category *every* morphism is an equivalence. 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.

Last revised on June 8, 2019 at 04:22:43. See the history of this page for a list of all contributions to it.