Objets injectifs dans les catégories abéliennes
Objets quasi-injectifs dans une catégorie abélienne avec générateur et limites inductives exactes
Obstructions for deformations of complexes
We develop two approaches to obstruction theory for deformations of derived isomorphism classes of complexes of modules for a profinite group over a complete local Noetherian ring of positive residue characteristic.
Octahedra and braids
On a certain generalization of spherical twists
This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of -curves on threefolds, or deforming -objects introduced by D.Huybrechts and R.Thomas.
On categorical shape theory
On deformations of pasting diagrams.
On derived categories and derived functors.
On derived equivalence classification of gentle two-cycle algebras
We classify, up to derived (equivalently, tilting-cotilting) equivalence, all nondegenerate gentle two-cycle algebras. We also give a partial classification and formulate a conjecture in the degenerate case.
On generation of torsion theories
On generation of torsion theories: a correction
On Kurosh-Amitsur radicals of finite groups.
On -exact categories
An -exact category is a pair consisting of an additive category and a class of sequences with terms satisfying certain axioms. We introduce -weakly idempotent complete categories. Then we prove that an additive -weakly idempotent complete category together with the class of all contractible sequences with terms is an -exact category. Some properties of the class are also discussed.
On Neeman's well generated triangulated categories.
On nonstandard tame selfinjective algebras having only periodic modules
We investigate degenerations and derived equivalences of tame selfinjective algebras having no simply connected Galois coverings but the stable Auslander-Reiten quiver consisting only of tubes, discovered recently in [4].
On n-permutable equivalence relations in regular categories
On pure global dimension of locally finitely presented Grothendieck categories
On pure quotients and pure subobjects
In the theory of accessible categories, pure subobjects, i.e. filtered colimits of split monomorphisms, play an important role. Here we investigate pure quotients, i.e., filtered colimits of split epimorphisms. For example, in abelian, finitely accessible categories, these are precisely the cokernels of pure subobjects, and pure subobjects are precisely the kernels of pure quotients.
On pure semi-simple Grothendieck categories I
On pure semi-simple Grothendieck categories II