In this chapter we define and give the main properties of triangulated categories and
cohomological functors and prove in particular that the localization of a triangulated category …

In this chapter we introduce triangulated categories. These provide the appropriate
framework for studying derived functors and derived categories. A triangulated category is …

In this paper we discuss the Brown Representability Theorem for triangulated categories
having arbitrary coproducts. This theorem is an extremely useful tool and various versions …

In this paper, we give a short introduction to the theory of triangulated categories. We
present the relevant definitions and properties of triangulated categories which we use to …

Abstract LET T BE A COMPACTLY GENERATED TRIANGULATED CATEGORY WHICH IS
CLOSED UNDER ARBITRARY SMALL COPRODUCTS. BASED ON A CONSTRUCTION OF …

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 …

In this chapter we study the unbounded derived categories of Grothendieck categories,
using the results of Chap. 9. We prove the existence of enough homotopically injective …

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 …

In this paper, we consider the Brown representability theorem for triangulated categories
which are closed under coproducts of arbitrary size. We prove that every triangulated …

Recently a notion of support and a construction of local cohomology functors for [TR5]
compactly generated triangulated categories were introduced and studied by Benson …