Kerodon

Remark 2.1.4.22. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be nonunital monoidal categories. We can summarize Proposition 2.1.4.21 more informally as follows: for any functor $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}$, choosing a nonunital lax monoidal structure on $G$ is equivalent to choosing a nonunital monoidal structure on the oriented fiber product $\operatorname{\mathcal{C}}\operatorname{\vec{\times }}_{\operatorname{\mathcal{C}}} \operatorname{\mathcal{D}}$ which is compatible with the existing nonunital monoidal structures on $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$, respectively.