We survey the set–theoretic methods of module theory that make it possible to equip roots of
the contravariant Ext functor with filtrations built from the small roots. The power of these …

Let R be a commutative noetherian local ring. As an analog of the notion of the dimension of
a triangulated category defined by Rouquier, the notion of the dimension of a subcategory of …

We analyze Auslander-Reiten quivers of functorially finite resolving subcategories. Chapter
1 gives a short introduction into the basic definitions and theorems of Auslander-Reiten …

We start by surveying the tools of set–theoretic homological algebra that make it possible to
deconstruct roots of the contravariant Ext functor, ie., express them as transfinite extensions …

Modules M such that Ext R(M,−) Commutes with Direct Limits Page 1 Algebr Represent Theor
(2013) 16:1799–1808 DOI 10.1007/s10468-012-9382-y Modules M such that Ext 1 R(M,−) …

We prove that certain subcategories of, consisting of complete modules having a quasi-
Verma flag with respect to a Levi subalgebra, admit a combinatorial description similar to …

We relate the theory of purity of a locally finitely presented category with products to the
study of exact structures on the full subcategory of finitely presented objects. Properties in …

For each deconstructible class of modules $\mathcal D $, we prove that the categoricity of
$\mathcal D $ in a big cardinal is equivalent to its categoricity in a tail of cardinals. We also …

We obtain Morita invariant versions of Eilenberg-Watts type theorems, relating Deligne
products of finite linear categories to categories of left exact as well as of right exact functors …

Tilting modules appear in a variety of ways: their first definition was in the context of finite
dimensional algebras over a field. Later, they appeared naturally in applications of the …