Definition 13.3.1. An \(\infty \)-category \(C\) is called extensive if it admits finite coproducts and, for every \(n \geq 0\) and every collection of objects \(X_1, \dots , X_n\), the coproduct functor \[ \prod _{i=1}^n C_{/X_i} \longrightarrow C_{/\coprod _i X_i} \] is an equivalence.
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