4 papers · 1 filter
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…
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…
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…