Definition 4.2.20 (Finite \(\infty \)-categories). We denote by \[ \Cat ^{\fin }_{\infty } \subseteq \Cat _{\infty } \] the smallest full subcategory which contains the \(\infty \)-categories \(\emptyset \), \(*\) and \([1]\), and which is closed under pushouts of \(\infty \)-categories. A small \(\infty \)-category \(I\) is called finite if it is contained in \(\Cat ^{\fin }_{\infty }\).
Generated from the authoritative LaTeX source.