Warning 6.1.4.5. In the situation of Corollary 6.1.4.4, it is possible for the unit $\eta : \operatorname{id}_{C} \Rightarrow g \circ f$ to be an isomorphism while the counit $\epsilon : f \circ g \Rightarrow \operatorname{id}_{D}$ is not, or vice versa (in which case, the $1$-morphisms $f$ and $g$ cannot be isomorphisms).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$