# Kerodon

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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.