Remark 1.5.6.5. Let $f: A \rightarrow B$ be an inner anodyne map of simplicial sets. Then $f$ is a monomorphism. This follows from the observation that the collection of monomorphisms is weakly saturated (Proposition 1.5.5.14), since every inner horn inclusion $\Lambda ^ n_ i \hookrightarrow \Delta ^ n$ is a monomorphism.
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