Locally rigid $\infty$-categories

Maxime Ramzi

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arXiv · 2410.21524

Locally rigid $\infty$-categories

Maxime Ramzi

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Abstract

We develop the theory of locally rigid and rigid symmetric monoidal $\infty$-categories over an arbitrary base $\mathcal{V}\in\mathrm{CAlg}(\mathbf{Pr}^\mathrm{L})$. Among other things, we prove that every locally rigid commutative $\mathcal{V}$-algebra arises as a ``completion'' of a rigid commutative $\mathcal{V}$-algebra. 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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BibTeX RIS

Maxime Ramzi. 2024-10-28. Locally rigid $\infty$-categories. https://arxiv.org/abs/2410.21524

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