Remark 4.1.1.7. The collection of inner fibrations is closed under filtered colimits. That is, if $\{ q_{\alpha }: X_{\alpha } \rightarrow S_{\alpha } \} $ is a filtered diagram in the arrow category $\operatorname{Fun}( [1], \operatorname{Set_{\Delta }})$ having colimit $q: X \rightarrow S$, and each $q_{\alpha }$ is an inner fibration of simplicial sets, then $q$ is also an inner fibration of simplicial sets.

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