Using six functor formalisms, the authors prove that hypercomplete locally compact ANR homology manifolds are cohomologically smooth, that compact ANR homology manifolds are Poincaré duality complexes with Spivak tangent fibration as dualizing sheaf, introduce homotopy manifolds, and show that homot
Universality of span 2-categories and the construction of 6-functor formalisms
4 Pith papers cite this work. Polarity classification is still indexing.
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Sheaf categories are the unique six functor formalisms on LCH spaces satisfying natural properties, implying equivalence for continuous formalisms.
The span functor from double ∞-categories to ∞-categories admits a right adjoint given by squares, yielding new proofs of equivalences among the Q-, S-, cobordism, and squares models of algebraic K-theory.
Introduces chromatic Euler characteristics for infinite groups with finite proper action models and proves associated duality and vanishing results in equivariant spectra.
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Homology manifolds via six functor formalisms
Using six functor formalisms, the authors prove that hypercomplete locally compact ANR homology manifolds are cohomologically smooth, that compact ANR homology manifolds are Poincaré duality complexes with Spivak tangent fibration as dualizing sheaf, introduce homotopy manifolds, and show that homot
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A characterization of sheaves among six functor formalisms on $\mathrm{LCH}$
Sheaf categories are the unique six functor formalisms on LCH spaces satisfying natural properties, implying equivalence for continuous formalisms.
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Chromatic Euler characteristics and duality for infinite groups
Introduces chromatic Euler characteristics for infinite groups with finite proper action models and proves associated duality and vanishing results in equivariant spectra.