Remark 3.1.1.7. The collection of Kan fibrations is closed under filtered colimits. That is, if $\{ f_{\alpha }: X_{\alpha } \rightarrow S_{\alpha } \} $ is any filtered diagram in the arrow category $\operatorname{Fun}( [1], \operatorname{Set_{\Delta }})$ having colimit $f: X \rightarrow S$, and each $f_{\alpha }$ is a Kan fibration of simplicial sets, then $f$ is also a Kan fibration of simplicial sets.

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