Kerodon

Remark 6.3.1.15 (Coproducts). Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a morphism of simplicial sets which is given as the coproduct of a collection of morphisms $\{ F_ i: \operatorname{\mathcal{C}}_ i \rightarrow \operatorname{\mathcal{D}}_ i \} _{i \in I}$. Suppose that each $F_{i}$ exhibits the simplicial set $\operatorname{\mathcal{D}}_{i}$ as a localization of $\operatorname{\mathcal{C}}_ i$ with respect to some collection of edges $W_{i}$ of $\operatorname{\mathcal{C}}_ i$. Then $F$ exhibits $\operatorname{\mathcal{D}}$ as a localization of $\operatorname{\mathcal{C}}$ with respect to $W = \bigcup _{i \in I} W_ i$.