§ 1. Motivation. For any unital ring R, let Mod (R) denote the category of (left) unitary R-
modules, ie satisfying 1m= m for all elements m. This category is important in many areas of …

Let R be a ring with 1# 0. R-Mod (resp. Mod-R} denotes the category of left (resp. rrght) R-
modules. Throughout the entrre article full subcategories of R-Mod (resp. Mod-R) will be …

The thesis studies dualities between categories of modules which are finitely closed, ie
closed under submodules, factor modules and finite direct sums. Omitting the requirement …

Definable subcategories may be extended along a ring homomorphism directly, by using
their defining conditions in the new module category, or by tensoring up with the new ring …

We develop the theory of presentable categories internal to an $\infty $-topos $\mathcal {B}
$. We provide several characterisations of these, including a description in terms of the …

In [R. Colpi, KR Fuller, Tilting objects in abelian categories and quasitilted rings, Trans.
Amer. Math. Soc., in press] tilting objects in an arbitrary abelian category H are introduced …

This is the second part of a study on model theory of modules begun in [RO]. Throughout, I
refer to that paper as “Part I”. I observed there a coincidence between some algebraic and …

Homological ring epimorphisms are often used in modern representation theory and
algebraic K-theory. In this paper, we give some new characterizations of when a universal …

Let D be a full subcategory of an abelian category A. We study the relation between the
following properties of the subcategory D.(1) The subcategory D is contravariantly finite in …