# Kerodon

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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.