Kerodon

Remark 7.6.1.6. Let $\operatorname{\mathcal{C}}$ be an ordinary category, and let $\{ q_ i: Y \rightarrow Y_ i \} _{i \in I}$ be a collection of morphisms in $\operatorname{\mathcal{C}}$. Then $\{ q_ i \} _{i \in I}$ exhibits $Y$ as a product of the collection $\{ Y_ i \} _{i \in I}$ in the category $\operatorname{\mathcal{C}}$ (in the sense of classical category theory) if and only if it exhibits $Y$ as a product of the collection $\{ Y_ i \} _{i \in I}$ in the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ (in the sense of Definition 7.6.1.3).