Remark 4.7.4.8. 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 4.7.3.4.