# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Remark 5.4.0.5. Throughout this book, we will make reference to a dichotomy between “small” and “large” mathematical objects. We will generally take a somewhat informal view of this dichotomy, taking care only to avoid maneuvers which are obviously illegitimate (see Example 5.4.0.1). However, the reader who wishes to adopt a more scrupulous approach could proceed (within the framework of Zermelo-Fraenkel set theory) as follows:

• Assume the existence of an uncountable strongly inaccessible cardinal $\kappa$ (see Definition 5.4.3.20).

• Declare that an $\infty$-category $\operatorname{\mathcal{C}}$ is small (essentially small, locally small) if it is $\kappa$-small (essentially $\kappa$-small, locally $\kappa$-small), and apply similar conventions to other mathematical objects of interest (such as sets and categories).