(infinity,0)-category

- homotopy hypothesis-theorem
- delooping hypothesis-theorem
- periodic table
- stabilization hypothesis-theorem
- exactness hypothesis
- holographic principle

- (n,r)-category
- Theta-space
- ∞-category/∞-category
- (∞,n)-category
- (∞,2)-category
- (∞,1)-category
- (∞,0)-category/∞-groupoid
- n-category = (n,n)-category
- n-poset = (n-1,n)-category
- n-groupoid = (n,0)-category

- categorification/decategorification
- geometric definition of higher category
- algebraic definition of higher category
- stable homotopy theory

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 August 25, 2021 at 05:19:50. See the history of this page for a list of all contributions to it.