Kerodon

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

Remark 4.7.3.4. Let $\kappa $ be a cardinal and let $T$ be a $\kappa $-small set. Then:

  • Any subset of $T$ is also $\kappa $-small (see Proposition 4.7.2.3).

  • The set $T$ is $\lambda $-small for every cardinal $\lambda \geq \kappa $.

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