We study the small and big finitistic projective, injective and flat dimensions over a non-
positively graded commutative noetherian DG-ring $ A $ with bounded cohomology. Our …

We give an account of model theory in the context of compactly generated triangulated and
tensor-triangulated categories ${\cal T} $. We describe pp formulas, pp-types and free …

We systematically develop, study, and give applications of definable functors between
compactly generated triangulated categories. Such functors preserve pure triangles, pure …

For a ring $ A $, we consider the question whether every bounded above cochain complex
of injective $ A $-modules which is acyclic is null-homotopic. We show that if $ A $ is left and …

In a compactly generated triangulated category, we introduce a class of tilting objects
satisfying a certain purity condition. We call these the decent tilting objects and show that the …

We develop an alternative approach to the homological spectrum through the lens of
definable subcategories. This culminates in a proof that the homological spectrum is …