Remark The collections of left and right are closed under filtered colimits. That is, suppose we are given a filtered diagram $\{ f_{\alpha }: X_{\alpha } \rightarrow S_{\alpha } \} $ in the arrow category $\operatorname{Fun}( [1], \operatorname{Set_{\Delta }})$, having colimit $f: X \rightarrow S$. If each $f_{\alpha }$ is a left fibration , then $f$ is also a left fibration. If each $f_{\alpha }$ is a right fibration, then $f$ is also a right fibration.