Recall that for a triangulated category T, a Bousfield localization is an exact functor L: T→ T
which is coaugmented (there is a natural transformation Id→ L; sometimes L is referred to as …

arXiv:0806.1324v2 [math.CT] 14 Mar 2009 Page 1 arXiv:0806.1324v2 [math.CT] 14 Mar 2009
LOCALIZATION THEORY FOR TRIANGULATED CATEGORIES HENNING KRAUSE Contents …

The aim of this paper is to develop a framework for localization theory of triangulated
categories\(\mathcal {C}\), that is, from a given extension-closed subcategory\(\mathcal {N}\) …

For a compactly generated triangulated category we gives a new proof for the fact that the
category of modules over its subcategory consisting of all compact objects it is not only the …

Given a cohomological functor from a triangulated category to an abelian category, we
construct under appropriate assumptions for any localization functor of the abelian category …

Given a thick subcategory of a triangulated category, we define a colocalisation and a
natural long exact sequence that involves the original category and its localisation and …

For a localizing class $$\mathcal {S} $$ of morphisms in a pretriangulated category
$$\mathcal {D} $$, a weak version of a sufficient condition that guarantees the transfer of the …

The ordinary localization of a category (along a family of morphisms) is a method used to
add inverse morphisms (for the given family), thus obtaining isomorphisms. This is …

We give an elementary introduction to the theory of triangulated categories covering their
axioms, homological algebra in triangulated categories, triangulated subcategories, and …

The purpose of a model category is to serve as a presentation of its homotopy theory (where
we loosely de ne the\homotopy theory" of a model category as its homotopy category …