131 citations · 953 across the 64 of their papers we have counts for
33 papers · 1 filter
Comodules and contramodules over coalgebras associated with locally finite categories
Leonid Positselski
We explain how to attach a coalgebra over a field to a small -linear category satisfying suitable finiteness conditions. In this context, we study f…
Fp-projective periodicity
Silvana Bazzoni, Michal Hrbek, Leonid Positselski
The phenomenon of periodicity, discovered by Benson and Goodearl, is linked to the behavior of the objects of cocycles in acyclic complexes. It is known that any flat $\mathsf{Proj…
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…
Differential graded Koszul duality: an introductory survey
Leonid Positselski
This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based on the author's memoir arXiv:0905.2621. The paper is intended to serve as a pedagogical intr…
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…
Derived, coderived, and contraderived categories of locally presentable abelian categories
Leonid Positselski, Jan Stovicek
For a locally presentable abelian category with a projective generator, we construct the projective derived and contraderived model structures on the category of comple…
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…
Unbounded derived categories of small and big modules: Is the natural functor fully faithful?
Leonid Positselski, Olaf M. Schnürer
Consider the obvious functor from the unbounded derived category of all finitely generated modules over a left noetherian ring to the unbounded derived category of all modules.…
Cofibrant generation of pure monomorphisms
Michael Lieberman, Leonid Positselski, Jiri Rosicky +1
We show that pure monomorphisms are cofibrantly generated---generated from a set of morphisms by pushouts, transfinite composition, and retracts---in any locally finitely presentab…
Topologically semisimple and topologically perfect topological rings
Leonid Positselski, Jan Stovicek
Extending the Wedderburn-Artin theory of (classically) semisimple associative rings to the realm of topological rings with right linear topology, we show that the abelian category…
Covers and direct limits: a contramodule-based approach
Silvana Bazzoni, Leonid Positselski
We present applications of contramodule techniques to the Enochs conjecture about covers and direct limits, both in the categorical tilting context and beyond. In the -tilting-c…
Pseudo-dualizing complexes of bicomodules and pairs of t-structures
Leonid Positselski
This paper is a coalgebra version of arXiv:1703.04266 and a sequel to arXiv:1607.03066. We present the definition of a pseudo-dualizing complex of bicomodules over a pair of coasso…
Contramodules over pro-perfect topological rings
Leonid Positselski
For four wide classes of topological rings , we show that all flat left -contramodules have projective covers if and only if all flat left -c…
Exactness of direct limits for abelian categories with an injective cogenerator
Leonid Positselski, Jan Stovicek
We prove that the exactness of direct limits in an abelian category with products and an injective cogenerator J is equivalent to a condition on J which is well-known to characteri…
Infinity-tilting theory
Leonid Positselski, Jan Stovicek
We define the notion of an infinitely generated tilting object of infinite homological dimension in an abelian category. A one-to-one correspondence between -tilting object…
Nearly locally presentable categories
Leonid Positselski, Jiri Rosicky
We introduce a new class of categories generalizing locally presentable ones. The distinction does not manifest in the abelian case and, assuming Vopenka's principle, the same happ…
The tilting-cotilting correspondence
Leonid Positselski, Jan Stovicek
To a big n-tilting object in a complete, cocomplete abelian category A with an injective cogenerator we assign a big n-cotilting object in a complete, cocomplete abelian category B…
Abelian right perpendicular subcategories in module categories
Leonid Positselski
We show that an abelian category can be exactly, fully faithfully embedded into a module category as the right perpendicular subcategory to a set of modules or module morphisms if…
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…
Smooth duality and co-contra correspondence
Leonid Positselski
The aim of this paper is to explain how to get a complex of smooth representations out of the dual vector space to a smooth representation of a p-adic Lie group, in natural charact…
Dedualizing complexes of bicomodules and MGM duality over coalgebras
Leonid Positselski
This paper is based on the material of Section 4 and Appendix C in arXiv:1503.05523v6, which was excluded from the subsequent versions of arXiv:1503.05523. We present the definitio…
Triangulated Matlis equivalence
Leonid Positselski
This paper is a sequel to arXiv:1503.05523 and arXiv:1605.03934. We extend the classical Harrison-Matlis module category equivalences to a triangulated equivalence between the deri…
Contraadjusted modules, contramodules, and reduced cotorsion modules
Leonid Positselski
This paper is devoted to the more elementary aspects of the contramodule story, and can be viewed as an extended introduction to the more technically complicated arXiv:1503.05523.…
Covers, envelopes, and cotorsion theories in locally presentable abelian categories and contramodule categories
Leonid Positselski, Jiri Rosicky
We prove general results about completeness of cotorsion theories and existence of covers and envelopes in locally presentable abelian categories, extending the well-established th…