The most commonly known triangulated categories arise from chain complexes in an
abelian category by passing to chain homotopy classes or inverting quasi-isomorphisms …

Right triangulated categories can be thought of as triangulated categories whose shift
functor is not an equivalence. We give intrinsic characterisations of when such categories …

In this article, we show that the localization of an extriangulated category by a multiplicative
system satisfying mild assumptions can be equipped with a natural, universal structure of an …

Recollements were introduced originally by Beilinson, Bernstein and Deligne to study the
derived categories of perverse sheaves, and nowadays become very powerful in …

Torsion pairs in recollements of abelian categories Page 1 Front. Math. China 2018, 13(4):
875–892 https://doi.org/10.1007/s11464-018-0712-1 Torsion pairs in recollements of abelian …

We call a triangulated category hereditary, in case it is triangle equivalent to the bounded
derived category Db (A) of a hereditary abelian category A. Such a hereditary triangulated …

We show that if a (not necessarily algebraic) triangulated category T contains an admissible
hereditary abelian subcategory H, then we can lift the inclusion of H into T to a fully faithful …

We investigate several homological aspects of recollements of abelian categories. In
particular, we study how various homological invariants and dimensions of the categories …

The concept of a morphism determined by an object provides a method to construct or
classify morphisms in a fixed category. We show that this works particularly well for …