Vopěnka's principle in $\infty$-categories

Abstract

In this article, the interplay between Vopěnka'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) Vopěnka's principle have on the detection of reflexive subcategories of a presentable categories can be generalized to $\infty$-categories.

22 pages, any comments are welcome!