131 citations · 953 across the 64 of their papers we have counts for
7 papers · 1 filter
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…
On strongly flat and weakly cotorsion modules
Leonid Positselski, Alexander Slavik
The aim of this paper is to describe the classes of strongly flat and weakly cotorsion modules with respect to a multiplicative subset or a finite collection of multiplicative subs…
Flat morphisms of finite presentation are very flat
Leonid Positselski, Alexander Slavik
Principal affine open subsets in affine schemes are an important tool in the foundations of algebraic geometry. Given a commutative ring , -modules built from the rings of…
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…