Dualizable additive categories are characterized intrinsically and via almost modules, and a universal finitary localizing invariant (prestable motives) is constructed whose unit corepresents algebraic K-theory.
Module-theoretic approach to dualizable Grothendieck categories
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We prove that every dualizable Grothendieck category whose dual is again a Grothendieck category satisfies Grothendieck's conditions Ab6 and Ab4*, by taking a module-theoretic approach based on the Gabriel-Popescu embedding. Combining this with a result by Stefanich, we conclude that the class of dualizable linear cocomplete categories is precisely the class of linear Grothendieck category satisfying Ab6 and Ab4*. This provides a complete answer to a modified conjecture on the dualizability, originally posed by Brandenburg, Chirvasitu, and Johnson-Freyd.
fields
math.AT 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Dualizable Additive Categories
Dualizable additive categories are characterized intrinsically and via almost modules, and a universal finitary localizing invariant (prestable motives) is constructed whose unit corepresents algebraic K-theory.