The $\infty$-Categorical Reflection Theorem and Applications

Abstract

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