Mann’s six-functor formalism conjecture

Mann’s conjecture asks whether every six-functor formalism extends to the specified lax symmetric monoidal functor on the relevant $(\infty,2)$-category.

Known results

• Cnossen–Lenz–Linskens established an earlier special case, which the new work generalizes.

Recent preprint

Carmeli, Kapon, and Nissan state that their Theorem B implies Mann’s conjecture via Corollary 6.2.7, constructing the extension through internal higher algebra. A separate paper gives an independent treatment of the corresponding $(I,P)$-biadjointable construction and applies it to $\mathbb{D}=\mathrm{Cat}_\infty$. The preprint credits ChatGPT Astra (OpenAI) with checking arguments and proofreading, including corrections to three propositions; the authors retain responsibility for the proof.

Current status (as of September 2026): A preprint claims the conjecture proved and a separate paper reports an independent proof of the corresponding result, but the resolution remains unverified; no counterexample is recorded.