Related papers: Unbounded Weight Structures: (Re)construction and …

In this work we study the notions of structural and universal completeness both from the algebraic and logical point of view. In particular, we provide new algebraic characterizations of quasivarieties that are actively and passively…

We first study the weight structure on the triangulated category of Artin-Tate motives over a perfect base field k, building on results of Bondarko's. We then study the t-structure on the triangulated category of Artin-Tate motives, when k…

We develop the theory of exact completions of regular $\infty$-categories, and show that the $\infty$-categorical exact completion (resp. hypercompletion) of an abelian category recovers the connective half of its bounded (resp. unbounded)…

With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordered structures. The approach also allows us to encode notions…

We establish rigid tensor category structure on finitely-generated weight modules for the subregular $W$-algebras of $\mathfrak{sl}_n$ at levels $ - n + \frac{n}{n+1}$ (the $\mathcal{B}_{n+1}$-algebras of Creutzig-Ridout-Wood) and at levels…

We show that, under particular conditions, if a t-structure in the unbounded derived category of a locally coherent Grothendieck category restricts to the bounded derived category of its category of finitely presented objects, then its…

Consider a diagram of quasi-categories that admit and functors that preserve limits or colimits of a fixed shape. We show that any weighted limit whose weight is a projective cofibrant simplicial functor is again a quasi-category admitting…

Recently, Amnon Neeman settled a bold conjecture by Antieau, Gepner, and Heller regarding the relationship between the regularity of finite-dimensional noetherian schemes and the existence of bounded $t$-structures on their derived…

Given a suitable Noetherian scheme, we classify tensor $t$-structures on the bounded derived category of coherent sheaves and its variants with prescribed support. Furthermore, we show that the existence of such $t$-structures restricting…

The (co)completeness problem for the (projectively) stable module category of an associative ring is studied. (Normal) monomorphisms and (normal) epimorphisms in such a category are characterized. As an application, we give a criterion for…

In the paper "Deformation theory of abelian categories", the last two authors proved that an abelian category with enough injectives can be reconstructed as the category of finitely presented modules over the category of its injective…

In this paper, we construct a monoidal weight structure on the stable $\infty$-category of rigid analytic motives over a local field $K$ via Galois descent. This extends the weight structure on the full subcategory of rigid analytic motives…

We study "canonical weight decompositions" slightly generalizing that defined by J. Wildeshaus. For an triangulated category $C$, any integer $n$, and a weight structure $w$ on $C$ a triangle $LM\to M\to RM\to LM[1]$, where $LM$ is of…

We show that Klemenc's stable envelope of exact $\infty$-categories induces an equivalence between stable $\infty$-categories with a bounded heart structure and weakly idempotent complete exact $\infty$-categories. Moreover, we generalise…

Let $\mathfrak{g}$ be a symmetrizable Kac-Moody algebra, $U_q(\mathfrak{g})$ its quantum group, and $U_q(\mathfrak{k}) \subset U_q(\mathfrak{g})$ a quantum symmetric pair subalgebra determined by a Lie algebra automorphism $\theta$. We…

We develop a general theory of 3-dimensional ``orbifold completion'', to describe (generalised) orbifolds of topological quantum field theories as well as all their defects. Given a semistrict 3-category $\mathcal{T}$ with adjoints for all…

We describe the heart of the canonical $t$-structure on the perfect derived category of a strictly positive graded algebra as the module category over the quadratic dual. Applying this result we obtain examples showing new phenomena on…

In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefevre's thesis.…

Let $X$ be a finite-dimensional, noetherian scheme. Antieau, Gepner and Heller conjectured that its derived category of perfect complexes has a bounded t-structure if and only if $X$ is regular. We prove a generalization, and to do so we…

We construct an invariant of t-structures on the derived category of a Noetherian ring. This invariant is complete when restricting to the category of quasi-coherent complexes, and also gives a classification of nullity classes with the…