Localisation and colocalisation of triangulated categories at thick subcategories (Q2879615)

The localisation of a triangulated category (modulo thick subcategories) is an important tool in the study of various kind of triangulated categories. In this paper the authors introduce and study a dual notion, called the right colocalisation of a homological functor \(F:\mathcal{T}\to Ab\), where \(\mathcal{T}\) is a triangulated category and \(Ab\) is the category of all abelian groups (Definition 3.3). The principal properties of these functors are proved: the localization functor is homological (Theorem 3.4), and it induces some natural long exact sequences in \(Ab\) (Theorem 4.2).