PreprintCC BY 4.0arXiv
Six functor formalisms via internal higher algebra
Abstract
We extend a six-functor formalism D:Span(C,E)→Cat to a lax symmetric monoidal functor of (∞,2)-categories Span2(C,E)PI→Cat, where P and I are the classes of D-proper and D-étale morphisms, respectively. This proves a conjecture of Mann and generalizes a special case of a theorem of Cnossen, Lenz, and Linskens. To prove this result, we develop a theory of internal E-monoidal categories and E-operads, where E is a local class of morphisms in an ∞-topos. These notions generalize the internal symmetric monoidal categories and operads developed by Martini and Wolf.
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BibTeX
@misc{carmeli2026functor,
title = {{Six functor formalisms via internal higher algebra}},
author = {Shachar Carmeli and Guy Kapon and Noam Nissan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37520},
eprint = {2609.37520},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37520},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Six functor formalisms via internal higher algebra
AU - Shachar Carmeli
AU - Guy Kapon
AU - Noam Nissan
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37520
UR - https://arxiv.org/abs/2609.37520
AB - We extend a six-functor formalism D:Span(C,E)→Cat to a lax symmetric monoidal functor of (∞,2)-categories Span^2(C,E)^P_I→Cat, where P and I are the classes of D-proper and D-étale morphisms, respectively. This proves a conjecture of Mann and generalizes a special case of a theorem of Cnossen, Lenz, and Linskens. To prove this result, we develop a theory of internal E-monoidal categories and E-operads, where E is a local class of morphisms in an ∞-topos. These notions generalize the internal symmetric monoidal categories and operads developed by Martini and Wolf.
ER -