arXiv:1308.0113v1 [math.CT] 1 Aug 2013 Page 1 arXiv:1308.0113v1 [math.CT] 1 Aug 2013 THE
DUAL OF THE HOMOTOPY CATEGORY OF PROJECTIVE MODULES SATISFIES BROWN …

For a triangulated category with products we prove a formal criterion in order to satisfy
Brown representability for covariant functors. We apply this criterion for showing that both …

We prove that a right $ R $-module $ M $ is $\Sigma $-pure injective if and only if $\mathrm
{Add}(M)\subseteq\mathrm {Prod}(M) $. Consequently, if $ R $ is a unital ring, the homotopy …

The homotopy category of complexes of projective modules Page 1 Advances in Mathematics
193 (2005) 223–232 www.elsevier.com/locate/aim The homotopy category of complexes of …

We call product generator of an additive category a fixed object satisfying the property that
every other object is a direct factor of a product of copies of it. In this paper we start with an …

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 …

We classify all the localizing subcategories of the derived category D (R) of modules over a
noetherian ring R, after developing the theory of unbounded complexes over R. Then, we …

Let R be any ring with identity. We show that the homotopy category of all acyclic chain
complexes of pure-projective R-modules is a compactly generated triangulated category …

We show that for the homotopy category K (Ab) of complexes of abelian groups, both Brown
representability and Brown representability for the dual fail. We also provide an example of a …

We introduce the notion of balanced pair of additive subcategories in an abelian category.
We give sufficient conditions under which a balanced pair of subcategories gives rise to a …