Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 1.1.8.16. In the statement of Lemma 1.1.8.15, we can replace $(3)$ by the following pair of conditions:

$(3')$

For each $n \geq 0$, the standard $n$-simplex $\Delta ^ n$ belongs to $\operatorname{\mathcal{U}}$.

$(3'')$

The subcategory $\operatorname{\mathcal{U}}\subseteq \operatorname{Set_{\Delta }}$ is closed under the formation of coproducts.