The ∞-categorical reflection theorem and applications

Shaul Ragimov; Tomer M. Schlank

doi:10.1112/topo.70060

The ∞-categorical reflection theorem and applications

Shaul Ragimov^*
, Tomer M. Schlank

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We prove an (Formula presented.) -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 (Formula presented.) -category that is closed under limits and (Formula presented.) -filtered colimits is a presentable (Formula presented.) -category. We then use this theorem in order to classify subcategories of a symmetric monoidal (Formula presented.) -category that are equivalent to a category of modules over an idempotent algebra.

Original language	English
Article number	e70060
Journal	Journal of Topology
Volume	19
Issue number	1
DOIs	https://doi.org/10.1112/topo.70060
State	Published - Mar 2026
Externally published	Yes

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© 2025 The Author(s). Journal of Topology is copyright © London Mathematical Society.

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The ∞-categorical reflection theorem and applications

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