Recollements were introduced originally by Beilinson, Bernstein and Deligne to study the
derived categories of perverse sheaves, and nowadays become very powerful in …

During the 1960s considerable work was done in order to understand the meaning of
“epimorphism”. The notion plays an important role in categories of rings where the abstract …

Starting with a Grothendieck category $\mathcal {G} $ and a torsion pair $\mathbf
{t}=(\mathcal {T},\mathcal {F}) $ in $\mathcal G $, we study the local finite presentability and …

We classify complactly generated t-structures on the derived category of modules over a
commutative Noetherian ring R in terms of decreasing filtrations by supports on Spec (R). A …

We show that, over an arbitrary commutative ring, the localizations of the categories of dg
categories, of unital and of strictly unital $ A_\infty $ categories with respect to the …

Let R be a commutative ring with a 1. Original work by H. Fitting showed how we can
associate to each finitely generated E-module a unique sequence of R-ideals, which are …

All rings considered have non zero identity elements, are associative but non necessarily
commutative. All modules are unitary and are left modules over the ring in question. Let R be …

Given a small abelian category $\mathcal {A} $, the Freyd-Mitchell embedding theorem
states the existence of a ring $ R $ and an exact full embedding $\mathcal {A}\rightarrow R …

We propose a definition of when a triangulated category should be considered a complete
intersection. We show (using work of Avramov and Gulliksen) that for the derived category of …