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 study triangulated categories and torsion theories in them, and compare two definitions
of torsion theories in this work. The most important types of torsion theories—weight …

arXiv:2308.10815v1 [math.CT] 21 Aug 2023 Page 1 UNIVERSAL SUPPORT FOR
TRIANGULATED CATEGORIES PAUL BALMER AND PABLO S. OCAL Abstract. We revisit a …

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 …

These notes give a short survey of the approach to support theory and the study of lattices of
triangulated subcategories through the machinery of tensor triangular geometry. One main …

Recently, Amnon Neeman settled a bold conjecture by Antieau, Gepner, and Heller
regarding the relationship between the regularity of finite-dimensional noetherian schemes …

We define duality triples and duality pairs in compactly generated triangulated categories
and investigate their properties. This enables us to give an elementary way to determine …

We extend Deligne's notion of determinant functor to tensor triangulated categories.
Specifically, to account for the multiexact structure of the tensor, we define a determinant …

We give a simultaneous generalization of exact categories and triangulated categories,
which is suitable for considering cotorsion pairs, and which we call extriangulated …

The aim of this thesis is to investigate definability in monoidal additive categories. Given a
monoidal finitely accessible category C, satisfying certain assumptions, we prove that there …