Kerodon

Warning 7.6.1.2. Let $\operatorname{\mathcal{C}}$ be an $\mathrm{h} \mathit{\operatorname{Kan}}$-enriched category, and let $\{ q_ i: Y \rightarrow Y_ i \} _{i \in I}$ be a collection of morphisms in $\operatorname{\mathcal{C}}$. If $\{ q_ i \} _{i \in I}$ exhibits $Y$ as an $\mathrm{h} \mathit{\operatorname{Kan}}$-enriched product of $\{ Y_ i \} _{i \in I}$, then it also exhibits $Y$ as a product of the collection $\{ Y_ i \} _{i \in I}$ in the underlying category $\operatorname{\mathcal{C}}$ (where we neglect its $\mathrm{h} \mathit{\operatorname{Kan}}$-enrichment). Beware that the converse is false in general (see Warning 7.6.1.12).