Grothendieck construction and descent

Example 23.7.10 (Grothendieck construction). Let \(T\) be an \(\infty \)-topos. Given an anima \(A \in \An \), we obtain an equivalence \[ \Fun (A,T) \quad =\quad \lim _A T_{/*} \quad \simeq \quad T_{/\,\colim _A *}. \] We refer to this equivalence as the Grothendieck construction.