Kerodon

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

Corollary 7.7.4.11. Let $\kappa $ be an infinite cardinal and let $\operatorname{\mathcal{C}}$ be an $\infty $-category which admits pullbacks and $\kappa $-small coproducts. The following conditions are equivalent:

$(1)$

In the $\infty $-category $\operatorname{\mathcal{C}}$, $\kappa $-small coproducts are strongly universal.

$(2)$

In the $\infty $-category $\operatorname{\mathcal{C}}$, $\kappa $-small coproducts are universal and finite coproducts are strongly universal.

$(3)$

In the $\infty $-category $\operatorname{\mathcal{C}}$, $\kappa $-small coproducts are universal and coproducts are disjoint.