Universality of span 2-categories and the construction of 6-functor formalisms Article Swipe
Bastiaan Cnossen
,
Tobias Lenz
,
Sil Linskens
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2505.19192
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2505.19192
Given an $\infty$-category $C$ equipped with suitable wide subcategories $I, P \subset E\subset C$, we show that the $(\infty,2)$-category $\text{S}{\scriptstyle\text{PAN}}_2(C,E)_{P,I}$ of higher (or iterated) spans defined by Haugseng has the universal property that 2-functors $\text{S}{\scriptstyle\text{PAN}}_2(C,E)_{P,I} \to \mathbb D$ correspond precisely to $(I, P)$-biadjointable functors $C^\text{op} \to \mathbb D$, i.e. functors $F$ where $F(i)$ for $i \in I$ admits a left adjoint and $F(p)$ for $p \in P$ admits a right adjoint satisfying various Beck-Chevalley conditions. We also extend this universality to the symmetric monoidal and lax symmetric monoidal settings. This provides a conceptual explanation for - and an independent proof of - the Mann-Liu-Zheng construction of 6-functor formalisms from suitable functors $C^\text{op}\to\text{CAlg}(\text{Cat})$.
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- en
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- http://arxiv.org/abs/2505.19192
- https://arxiv.org/pdf/2505.19192
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Universality of span 2-categories and the construction of 6-functor formalismsWork title
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Bastiaan Cnossen, Tobias Lenz, Sil LinskensList of authors in order
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https://arxiv.org/abs/2505.19192Publisher landing page
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