Finally, let B and 8 be two rings, let 9 be a full subcategory of left R-modules closed under
direct sums and factor modules, let be a full subcategory of left S-modules containing ss and …

Given any Grothendieck category G, we study the notion of a tilting object of G, proving some
basic facts of tilting theory in this general setting. Our results apply, for instance, to …

Let $ R $ be a ring and $\mathcal C $ be a cotilting class of $ R $–modules. Define $ A\leq B
$ by $ A\subseteq B $ and $ A, B, B/A\in\mathcal C $. Then $(\mathcal C,\leq) $ is an …

In this dissertation, let B be a triangulated category and let D be an extension-closed
subcategory of B. First, we give some new characterizations of an Auslander-Reiten triangle …

Let $\mathcal {A} $ be a small dg category over a field $ k $ and let $\mathcal {U} $ be a
small full subcategory of the derived category $\mathcal {D}\mathcal {A} $ which generates …

By a well known theorem of K. Morita, any equivalence between full module categories over
rings R and S, are given by a bimodule RPS, such that RP is a finitely generated projective …

Given a bimodule M over an exact category C, we define an exact category CM with a
projection to C. This construction classifies certain split square-zero extensions of exact …

In this paper we expose some recent results (see References) on equivalences between
categories of modules. Let A e R be two rings, DA and GR subcategories of Mod-A and Mod …

We revisit a construction of wide subcategories going back to work of Ingalls and Thomas.
To a torsion pair in the category $ R\operatorname {-}\operatorname {mod} $ of finitely …

We classify 1-tilting classes over an arbitrary commutative ring. As a consequence, we
classify all resolving subcategories of finitely presented modules of projective dimension at …