Related papers: Mutation pairs and triangulated quotients

Let $R$ be a commutative ring. We introduce the notion of support of objects in an $R$-linear triangulated category. As an application, we study the non-existence of Bridgeland stability conditions on $R$-linear triangulated categories.

In this note we show that the known relation between double groupoids and matched pairs of groups may be extended, or seems to extend, to the triple case. The references give some other occurrences of double groupoids.

Given a fixed tensor triangulated category S we consider triangulated categories T together with an S-enrichment which is compatible with the triangulated structure of T. It is shown that, in this setting, an enriched analogue of Brown…

We provide a complete description of the category of pseudo-categories (including pseudo-functors, natural and pseudo-natural transformations and pseudo modifications). A pseudo-category is a non strict version of an internal category. It…

We classify the "quotients" of a tannakian category in which the objects of a tannakian subcategory become trivial, and we examine the properties of such quotient categories.

These notes provide an introduction to the theory of localization for triangulated categories. Localization is a machinery to formally invert morphisms in a category. We explain this formalism in some detail and we show how it is applied to…

Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…

Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In…

In the preceding part (I) of this paper, we showed that for any torsion pair (i.e., $t$-structure without the shift-closedness) in a triangulated category, there is an associated abelian category, which we call the heart. Two extremal cases…

We classify the module categories over the double (possibly twisted) of a finite group.

This paper is an expository account of the theory of stable infinity categories. We prove that the homotopy category of a stable infinity category is triangulated, and that the collection of stable infinity categories is closed under a…

We study cocoverings of triangulated categories, in the sense of Rouquier, and prove that for any regular cardinal $\alpha$ the condition of $\alpha$-compactness, in the sense of Neeman, is local with respect to such cocoverings. This was…

Generalizing the notion of matched pair of groups, we define and study matched pairs of locally compact groupoids endowed with Haar systems, in order to give new examples of measured quantum groupoids.

In this article, we initiate the study of hereditary extriangulated categories. Many important categories arising in representation theory in connection with various theories of mutation are hereditary extriangulated. Special cases include…

The quotient of a triangulated category modulo a subcategory was defined by Verdier. Motivated by the failure of the telescope conjecture, we introduce a new type of quotients for any triangulated category which generalizes Verdier's…

We study the uniqueness of enhancements of tensor-triangulated categories. To do so, we provide conditions under which these enhancements interact well with categorical decompositions. As an application we obtain new results about the…

We prove that there is an adjunction between what we call \'etale topological categories and restriction quantal frames that leads to an adjunction with a category of complete restriction monoids. This generalizes the adjunction between…

Coherence theorems for covariant structures carried by a category have traditionally relied on the underlying term rewriting system of the structure being terminating and confluent. While this holds in a variety of cases, it is not a…

We define the triangulated category of relative singularities of a closed subscheme in a scheme. When the closed subscheme is a Cartier divisor, we consider matrix factorizations of the related section of a line bundle, and their analogues…

Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, two conjectures on permutation polynomials proposed recently by Wu and Li [19] are…