arXiv subjects

Jun Maillard

Publications and source records attributed to Jun Maillard.

4 recordsLinked to original sources

arXiv2025

Torsion and complete dualizable objects in tensor-triangulated categories over a Noetherian ring

We study categories of dualizable torsion and complete objects for compactly-rigidly generated tensor-triangulated categories T with a Noetherian central action of a graded commutative Noetherian ring R. We show that they always admit a natural Noetherian action of the completed graded ring R^ and that the categories of dualizable torsion and complete objects can be abstractly reconstructed as tensor-triangulated R^-linear categories from the category of compact torsions objects with the corresponding structure. If the category of compact objects of T in addition admits a strong generator g, we show that the torsion coreflection (resp. complete reflection) of g is a strong generator for the category of dualizable torsion (resp. dualizable complete) objects. In that case, we also show that the categories of dualizable torsion and compact torsion objects determine each other in terms of Brown-type representability theorems.

math.CT↗

arXiv2025

Calabi-Yau property in derived Koszul calculus

A Poincar\'e Van den Bergh duality theorem for strong Kc-Calabi-Yau algebras was obtained by R. Taillefer and the first author under the assumption that the derived functors of functors involved in the statement exist. We prove the existence of these derived functors by showing that the dg category defining the derived Koszul calculus is isomorphic to a dg category of dg modules over a dg algebra. Therefore we get a definition of strong Kc-Calabi-Yau algebras and a corresponding duality theorem without any existence assumption. We prove that a polynomial algebra is strong Kc-Calabi-Yau.

math.RT↗

arXiv2021

A categorification of the Cartan-Eilenberg formula

We prove a categorification of the stable elements formula of Cartan and Eilenberg. Our formula expresses the derived category and the stable module category of a group as a bilimit of the corresponding categories for the $p$-subgroups.

math.RT↗

arXiv2021

On 2-final 2-functors

We present a criterion for $2$-final $(2,1)$-functors, analoguous to the classical one for final $1$-functor: a $(2,1)$-functor $F \colon A \to B$ is $2$-final if and only if, for any object $b$ of $B$, the slice $(2,1)$-category $b / F$ is nonempty, connected and simply connected. We also give a combinatorial presentation of paths and homotopies of paths in a $(2,1)$-category.

math.CT↗