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In this article, the interplay between Vop\v{e}nka's principle, as well asits 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 theconsequences that (weak) Vop\v{e}nka's principle have on the detection ofreflexive subcategories of a presentable categories can be generalized to$\infty$-categories.

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