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arXiv · 2207.09244

The $\infty$-Categorical Reflection Theorem and Applications

Shaul Ragimov·Tomer M. Schlank
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Abstract

We prove an $\infty$-categorical version of the reflection theorem of Ad\'amek-Rosick\'y. Namely, that a full subcategory of a presentable $\infty$-category which is closed under limits and $\kappa$-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.

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Shaul Ragimov, Tomer M. Schlank. 2022-07-19. The $\infty$-Categorical Reflection Theorem and Applications. https://doi.org/10.1112/topo.70060

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