Vop\v{e}nka's principle in $\infty$-categories

Abstract

In this article, the interplay between Vop\v{e}nka's principle, as well as its weaker counterpart, and presentable $\infty$-categories is studied. Analogous statements, arising after replacing categories with $\infty$-categories in the original ones, are introduced and compared to these. Further, the attention is focused on the question of to what extent the consequences that (weak) Vop\v{e}nka's principle have on the detection of reflexive subcategories of a presentable categories can be generalized to $\infty$-categories.