Kerodon

Remark 9.1.6.5. Let $\kappa $ be an infinite cardinal and let $\operatorname{\mathcal{C}}$ be a $\kappa $-filtered $\infty $-category. If $\operatorname{\mathcal{C}}$ are $\kappa $ are small, then the partially ordered set $(A, \leq )$ constructed in the proof of Theorem 9.1.6.2 is also small. More generally, if $\operatorname{\mathcal{C}}$ is $\lambda $-small for some uncountable cardinal $\lambda $ which is of cofinality $> \kappa $ and exponential cofinality $\geq \kappa $, then the partially ordered set $(A, \leq )$ is also $\lambda $-small.