Corollary 2.10.
A category \(T\) is a topos if and only if it is presentable and \(I\)-indexed colimits are both effective and universal for every small category \(I\).
Higher Topos Theory Section 2.1: Topoi and descent
Corollary 2.10.
A category \(T\) is a topos if and only if it is presentable and \(I\)-indexed colimits are both effective and universal for every small category \(I\).