Kerodon

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

Remark 5.4.4.8. Let $\kappa $ be an infinite cardinal and let $T$ be a $\kappa $-small simplicial set. Then:

  • Every simplicial subset of $T$ is $\kappa $-small.

  • The simplicial set $T$ is $\lambda $-small for each $\lambda \geq \kappa $.

  • For every epimorphism of simplicial sets $T \twoheadrightarrow S$, the simplicial set $S$ is also $\kappa $-small.

See Remark 5.4.3.4.