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Locally rigid $\infty$-categories (2410.21524v1)

Published 28 Oct 2024 in math.CT, math.AT, and math.KT

Abstract: We survey the theory of locally rigid and rigid symmetric monoidal $\infty$-categories over an arbitrary base $\mathcal{V}\in\mathrm{CAlg}(\mathbf{Pr}\mathrm{L})$. Along the way, we introduce and study ``$\mathcal{V}$-atomic morphisms'', which are analogues of compact morphisms over an arbitrary base $\mathcal{V}$.

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References (14)
  1. The stack of local systems with restricted variation and geometric Langlands theory with nilpotent singular support. arXiv preprint arXiv:2010.01906, 2020.
  2. E𝐸Eitalic_E-theory is compactly assembled. arXiv preprint arXiv:2402.18228, 2024.
  3. Shay Ben Moshe. Naturality of the ∞\infty∞-Categorical Enriched Yoneda Embedding. arXiv preprint arXiv:2301.00601, 2023.
  4. Lax colimits and free fibrations in ∞\infty∞-categories. arXiv preprint arXiv:1501.02161, 2015.
  5. A study in derived algebraic geometry: Volume I: correspondences and duality, volume 221. American Mathematical Society, 2019.
  6. Hadrian Heine. An equivalence between enriched ∞\infty∞-categories and ∞\infty∞-categories with weak action. arXiv preprint arXiv:2009.02428, 2020.
  7. Hadrian Heine. A monadicity theorem for higher algebraic structures. arXiv preprint arXiv:1712.00555v4, 2023.
  8. Higher traces, noncommutative motives, and the categorified Chern character. Advances in Mathematics, 309:97–154, 2017.
  9. The categorified Grothendieck–Riemann–Roch theorem. Compositio Mathematica, 157(1):154–214, 2021.
  10. Sheaves on manifolds. Available at author’s webpage.
  11. Jacob Lurie. Higher topos theory. Princeton University Press, 2009.
  12. Jacob Lurie. Higher algebra, 2012.
  13. Maxime Ramzi. Dualizable presentable ∞\infty∞-categories. In preparation, 2024.
  14. Marco Volpe. Six functor formalism for sheaves with non-presentable coefficients. arXiv preprint arXiv:2110.10212, 2021.

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