Sheaf categories are the unique six functor formalisms on LCH spaces satisfying natural properties, implying equivalence for continuous formalisms.
$E$-theory of $X$-$C^{*}$-algebras and functor formalisms
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We show that $E$-theory for locally compact Hausdorff spaces constitutes a six-functor formalism which is equivalent to the six-functor formalism of $\mathrm{E}$-valued sheaves. We furthermore show that the $E$-theory category for locales that can be written as unions of finite open sublocales is equivalent to the category of $\mathrm{E}$-valued cosheaves.
fields
math.AT 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
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.