Example 8.1.10.8. In the situation of Definition 8.1.10.6, suppose that $L$ is the collection of all isomorphisms in $\operatorname{\mathcal{C}}$. Then condition $(1)$ is equivalent to the requirement that $U$ is an isofibration (Example 8.1.9.8), and condition $(3)$ is automatic. Similarly, if $R$ is the collection of all isomorphisms in $\operatorname{\mathcal{C}}$, then condition $(2)$ is the requirement that $U$ is an isofibration, and condition $(3)$ is automatic.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$