# Kerodon

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

Exercise 2.2.5.2. Check that the composition of lax functors is well-defined. That is, if $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ and $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ are lax functors between $2$-categories, then the identity and composition constraints $\epsilon ^{GF}_{X}$ and $\mu ^{GF}_{g,f}$ of Construction 2.2.5.1 are compatible with the unit constraints and associativity constraints of $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{E}}$, as required by Definition 2.2.4.5.