Warning 7.2.1.8. Let $g: \Delta ^1 \rightarrow \Delta ^0$ be the projection map and let $f: \{ 1\} \hookrightarrow \Delta ^1$ be the inclusion. Then $g$ and $g \circ f$ are left cofinal (Proposition 7.2.1.5). However, the morphism $f$ is not left cofinal, since it is not left anodyne (see Example 4.2.4.7). Consequently, the collection of left cofinal morphisms does not satisfy the two-out-of-three property.
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