Kerodon

Example 8.4.2.3. Let $\operatorname{\mathcal{S}}_{ \mathrm{cont} }$ denote the full subcategory of $\operatorname{\mathcal{S}}$ spanned by the contractible Kan complexes. Then $\operatorname{\mathcal{S}}_{ \mathrm{cont} }$ is a dense subcategory of $\operatorname{\mathcal{S}}$. This follows by applying Corollary 8.4.2.2 in the special case $\operatorname{\mathcal{C}}= \Delta ^0$. Moreover, the same assertion holds if we replace $\operatorname{\mathcal{S}}_{ \mathrm{cont} }$ by any nonempty subcategory of itself; for example, the full subcategory of $\operatorname{\mathcal{S}}$ spanned by the standard $0$-simplex $\Delta ^0$.