The main goal of this paper is to prove the following: for a triangulated category C and E⊂
ObjC there exists a cohomological functor F (with values in some abelian category) such that …

The paper is aimed at proving the following: for a triangulated category $\underline {C} $
and $ E\subset\mathrm {Obj}\underline {C} $, there exists a cohomological functor $ F $(with …

We initiate the study of derived functors in the setting of extriangulated categories. By using
coends, we adapt Yoneda's theory of higher extensions to this framework. We show that …

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 …

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 …

In this article we prove that all the inclusions between the'classical'and naturally defined full
triangulated subcategories of a weakly approximable triangulated category are intrinsic (in …

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 …

We give a general construction of triangulated categories as quotients of exact categories
where the exact structure is picked out by a triple of functors (F, L, R). This subsumes the …

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

We show that a right triangulated category is best behaved when its shift satisfies conditions
making it what we call a right semi-equivalence. We consider right triangulated categories …