Accessible quasi-category

In mathematics, especially category theory, an accessible quasi-category is a quasi-category in which each object is an ind-object on some small quasi-category. In particular, an accessible quasi-category is typically large. The notion is a generalization of an earlier 1-category version of it, an accessible category introduced by Adámek and Rosický.

Definition

An ∞-category is called accessible or more precisely -accessible if it is equivalent to the ∞-category of -ind objects on some small ∞-category for some regular cardinal.

Facts

A small ∞-category is accessible if and only if it is idempotent-complete.