• Interaction With Identities. Let $F\colon \mathcal{C}\to \mathcal{D}$ and $G\colon \mathcal{D}\to \mathcal{E}$ be functors. The diagram

    commutes, i.e. we have

    \[ \text{id}_{G}\mathbin {\star }\text{id}_{F}=\text{id}_{G\circ F}. \]

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