Kerodon

Remark 8.7.3.16. Let $\kappa < \lambda $ be infinite cardinals, where $\lambda $ is regular and has exponential cofinality $\geq \kappa $.. Then the collection of isomorphism classes of $\kappa $-small simplicial sets is $\lambda $-small. This follows from Proposition 4.7.4.20 (in the case where $\kappa $ is uncountable) and Variant 4.7.4.21 (in the case where $\kappa = \aleph _0$). Consequently, in the formulation of Proposition 8.7.3.15, we may assume without loss of generality that the collection of simplicial sets $\mathbb {K}$ is $\lambda $-small.