131 citations · 953 across the 64 of their papers we have counts for
5 papers · 1 filter
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…
Koszulity of cohomology = -ness + quasi-formality
Leonid Positselski
This paper is a greatly expanded version of Section 9.11 in arXiv:1006.4343. A series of definitions and results illustrating the thesis in the title (where quasi-formality means v…
Coherent rings, fp-injective modules, dualizing complexes, and covariant Serre-Grothendieck duality
Leonid Positselski
For a left coherent ring A with every left ideal having a countable set of generators, we show that the coderived category of left A-modules is compactly generated by the bounded d…
Dedualizing complexes and MGM duality
Leonid Positselski
We show that various derived categories of torsion modules and contramodules over the adic completion of a commutative ring by a weakly proregular ideal are full subcategories of t…
Contramodules
Leonid Positselski
Contramodules are module-like algebraic structures endowed with infinite summation (or, occasionally, integration) operations satisfying natural axioms. Introduced originally by Ei…