We investigate parametrizations of compactly generated t-structures, or more generally, t-
structures with a definable coaisle, in the unbounded derived category $\mathrm …

We consider the notion of stack, originally due to Grothendieck and Giraud [15], in the
intrinsic sense (of Lawvere [26, 27]), that is, relative to the class of all epimorphisms in a …

We analyze Auslander-Reiten quivers of functorially finite resolving subcategories. Chapter
1 gives a short introduction into the basic definitions and theorems of Auslander-Reiten …

We study $ t $-structures (on triangulated categories) that are closely related to weight
structures. A $ t $-structure couple $ t=(C_ {t\le 0}, C_ {t\ge 0}) $ is said to be adjacent to a …

Let X be a quasi-compact and quasi-separated (not necessarily semiseparated) scheme.
The category QcoX of all quasi-coherent sheaves of OX-modules has several different pure …

We extend the work of Balmer, associating filtrations of essentially small tensor triangulated
categories to certain dimension functions, to the setting of actions of rigidly-compactly …

This paper surveys the recent advances concerning the relations between triangulated (or
derived) categories and their dg enhancements. We explain when some interesting …

We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type $\text {FP} _n $ and studying their closure properties with respect to short …

In this paper, we construct a version of Auslander–Reiten sequences for the K (n)-local
stable homotopy category. In particular, the role of the Auslander–Reiten translation is …

We prove that the tensor category of quasi-coherent modules $\mathsf {Qcoh}(X\times_S Y)
$ on a fiber product of quasi-compact quasi-separated schemes is the bicategorical pushout …