Remark 4.2.3.14. Let $f: X \rightarrow Y$ and $g: Y \rightarrow Z$ be morphisms of simplicial sets, and suppose that $g$ is a left covering map. Then $f$ is a left covering map if and only if $g \circ f$ is a left covering map. Similarly, if $g$ is a right covering map, then $f$ is a right covering map if and only if $g \circ f$ is a right covering map. In particular, the collections of left and right covering maps are closed under composition.
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