5 papers · 1 filter
Contraherent cosheaves on schemes
Leonid Positselski
Contraherent cosheaves are globalizations of contraadjusted or cotorsion modules over commutative rings obtained by gluing together over a scheme, with the colocalization functors…
Pseudo-dualizing complexes and pseudo-derived categories
Leonid Positselski
The definition of a pseudo-dualizing complex is obtained from that of a dualizing complex by dropping the injective dimension condition, while retaining the finite generatedness an…
Exact DG-categories and fully faithful triangulated inclusion functors
Leonid Positselski
We construct an "almost involution" assigning a new DG-category to a given one, and use this construction to recover, say, the abelian category of graded modules over the graded ri…
Coderived and contraderived categories of locally presentable abelian DG-categories
Leonid Positselski, Jan Stovicek
The concept of an abelian DG-category, introduced by the first-named author in arXiv:2110.08237, unites the notions of abelian categories and (curved) DG-modules in a common framew…
Exact categories of topological vector spaces with linear topology
Leonid Positselski
We explain why the naive definition of a natural exact category structure on complete, separated topological vector spaces with linear topology fails. In particular, contrary to ar…