The ∞‐categorical reflection theorem and applications

Abstract We prove an ‐categorical version of the reflection theorem of AdÁmek and Rosický [Arch. Math. 25 (1989), no. 1, 89–94]. Namely, that a full subcategory of a presentable ‐category that is closed under limits and ‐filtered colimits is a presentable ‐category. We then use this theorem in order to classify subcategories of a symmetric monoidal ‐category that are equivalent to a category of modules over an idempotent algebra.