We show that Krause's recollement exists for any locally coherent Grothendieck category
whose derived category is compactly generated. As a source of such categories, we …

Liftable pairs of adjoint functors between braided monoidal categories in the sense of [GV1]
provide auto-adjunctions between the associated categories of bialgebras. Motivated by …

This work presents a way to associate a Grothendieck site structure to a category endowed
with a unique factorisation system of its arrows. In particular this recovers the Zariski and …

Given an associative ring R and a torsion pair (T, F) in the category of right R-modules, the
heartH (T, F) associated with (T, F) is an abelian subcategory of the bounded derived …

We associate a $ t $-structure to a family of objects in $\boldsymbol {\mathsf {D}}(\mathcal
{A}) $, the derived category of a Grothendieck category $\mathcal {A} $. Using general …

We characterize rings over which every cotorsion module is pure injective (Xu rings) in terms
of certain descending chain conditions and the Ziegler spectrum, which renders the classes …

A successful theme in the development of triangulated categories has been the study of
compact objects. A weak dual notion called 0-cocompact objects was introduced in …

In this paper, we prove that for a noetherian formal scheme \mathfrakX, its derived category
of sheaves of modules with quasi-coherent torsion homologies D_qct(\mathfrakX) is …

In this paper, for an underlying small category U endowed with a Grothendieck topology τ,
and a linear category a which is graded over U in the sense of [13], we define a natural …