Krause [19] has proved that the homotopy category K (R-PureProj) of pure projective
modules over an associative ring R is compactly generated and equivalent to the Verdier …

K-flatness for unbounded complexes of modules over a ring R was introduced by
Spaltenstein [27], as an analogue of the classical notion of flatness for modules. In this …

In this paper, we examine the class of K-absolutely pure complexes. These are the
complexes which are right orthogonal in the homotopy category K (R) to the acyclic …

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 …

We study the homotopy category of unbounded complexes with bounded homologies and
its quotient category by the homotopy category of bounded complexes. In the case of the …

Our goal is to understand certain categories of complexes over R in terms of categories of
complexes over the other three rings, and in particular to study the algebraic K-theory of …

Let T be a triangulated category with products. A subcategory S⊂ T is called colocalizing if it
is triangulated and closed under products. Given any class of objects T⊂ T, the smallest …

Let R be a ring with identity and C (R) denote the category of complexes of R-modules. In
this paper we study the homotopy categories arising from projective (resp. injective) …

Let R be a ring. We prove that the homotopy category K (R-Proj) is always \aleph_1-
compactly generated, and, depending on the ring R, it may or may not be compactly …

The quotient of a triangulated category modulo a subcategory was defined by Verdier.
Motivated by the failure of the telescope conjecture, we introduce a new type of quotients for …