Remark 7.1.5.21. Corollary 7.1.5.20 has an obvious counterpart for $U$-limit diagrams under the assumption that $U: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is a cocartesian fibration, which can be proved in the same way. It also has a more subtle counterpart for $U$-colimit diagrams when $U$ is a cocartesian fibration (or $U$-limit diagrams when $U$ is a cartesian fibration), which we will discuss in ยง7.3.9 (see Proposition 7.3.9.2).
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