- 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.

On model categories presenting $(\infty,0)$-categories, namely models for $\infty$-groupoids (such as the model structure on simplicial groupoids) akin to corresponding models for $(\infty,1)$-categories (such as the model structure on simplicial categories):

- Julia E. Bergner,
*Adding inverses to diagrams II: Invertible homotopy theories are spaces*, Homology, Homotopy Appl.**10**2 (2008) 175-193 [doi:10.4310/HHA.2008.v10.n2.a9, doi:0710.2254, erratum:doi:10.4310/HHA.2012.v14.n1.a15]

Last revised on April 25, 2023 at 08:18:49. See the history of this page for a list of all contributions to it.