The $\mathrm{\infty }$-Categorical Reflection Theorem and Applications

In this paper we prove an $\mathrm{\infty }$-categorical version of the reflection theorem of Adámek-Rosický. Namely, that a full subcategory of a presentable $\mathrm{\infty }$-category which is closed under limits and $\kappa$-filtered colimits is a presentable $\mathrm{\infty }$-category. We then use this theorem in order to classify subcategories of a symmetric monoidal $\mathrm{\infty }$-category which are equivalent to a category of modules over an idempotent algebra.