Definition 1.7.4. We say an \(\infty \)-category \(C\) admits all \(I\)-indexed (co)limits if for every functor \(F\colon I \to C\) there exists a (co)limit (co)cone for \(F\). If \(G\colon C \to D\) is a functor between \(\infty \)-categories that admit \(I\)-indexed (co)limits, then we say that \(G\) preserves \(I\)-indexed (co)limits if for every functor \(F\colon I \to C\), the functor \(G\) sends (co)limit (co)cones of \(F\) in \(C\) to (co)limit (co)cones of \(GF\) in \(D\).
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