The paper introduces 'suprematic spaces' and claims a fully faithful classification of certain six functor formalisms plus a universal factorization through animated S-stacks.
Tannaka Duality for Geometric Stacks
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abstract
We show that, under appropriate hypothesis, the groupoid of maps from S to an an algebraic stack X can be identified with a category of tensor functors from coherent sheaves on X to coherent sheaves on S. As an application, we show that if S is a proper variety over the field of complex numbers, then every ``analytic'' map from S to X is ``algebraic''.
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A Classification of Six Functor Formalisms via Structured Spaces
The paper introduces 'suprematic spaces' and claims a fully faithful classification of certain six functor formalisms plus a universal factorization through animated S-stacks.