Spectral sheaves on locally compact Hausdorff spaces are initial among continuous six-functor formalisms, forcing all such formalisms to agree with sheaf (co)homology and to satisfy a universal localizing-invariant formula.
The universal six-functor formalism
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Continuous six-functor formalism on locally compact Hausdorff spaces
Spectral sheaves on locally compact Hausdorff spaces are initial among continuous six-functor formalisms, forcing all such formalisms to agree with sheaf (co)homology and to satisfy a universal localizing-invariant formula.