Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 2.2.5.3. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ and $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ be lax functors of $2$-categories, and let $GF: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{E}}$ be their composition. Then:

  • If $F$ and $G$ are unitary, then the composition $GF$ is unitary.

  • If $F$ and $G$ are functors, then the composition $GF$ is a functor.

  • If $F$ and $G$ are strictly unitary, then the composition $GF$ is strictly unitary.

  • If $F$ and $G$ are strict functors, then the composition $GF$ is a strict functor.