Related papers: Relative stable categories and birationality

This is the first in a series of papers in which we study representations of the Brauer category and its allies. We define a general notion of triangular category that abstracts key properties of the triangular decomposition of a semisimple…

The filter quotient construction is a particular instance of a filtered colimit of categories. It has primarily been considered in the context of categorical logic, where it has been used effectively to construct non-trivial models, for…

In this paper we give necessary and sufficient conditions for a functor to be representable in a strongly generated triangulated category which has a linear action by a graded ring, and we discuss some applications and examples.

We show that if A is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to…

Two left noetherian rings $R$ and $S$ are said to be {\it singularly equivalent} if their singularity categories are equivalent as triangulated categories. The aim of this paper is to give a necessary condition for two commutative…

It is shown that the idempotent completion of the additive hull of the tensor product of the residue category of the category of paths of a locally finite quiver modulo an admissible ideal and a dualizing category is dualizing. Furthermore,…

We introduce pseudocubical objects with pseudoconnections in an arbitrary category, obtained from the Brown-Higgins structure of a cubical object with connections by suitably relaxing their identities, and construct a cubical analog of the…

Given a reductive Lie algebra over the complex numbers, we introduce a family of category which generalises the BGG category $\mathcal{O}$. We also classify the simple modules for some of these categories and prove a semisimplicity result.

We establish a Dwyer-Kan equivalence of relative categories of combinatorial model categories, presentable quasicategories, and other models for locally presentable (infinity,1)-categories. This implies that the underlying quasicategories…

We generalise partial results about the Yau-Tian-Donaldson correspondence on ruled manifolds to bundles whose fibre is a classical flag variety. This is done using Chern class computations involving the combinatorics of Schur functors. The…

We give necessary and sufficient conditions for stratification and costratification to descend along a coproduct preserving, tensor-exact $R$-linear functor between $R$-linear tensor-triangulated categories which are rigidly-compactly…

Let $\&$ be a continuous triangular norm on the unit interval $[0,1]$ and $\mathbf{A}$ be a cartesian closed and stable subconstruct of the category consisting of all real-enriched categories. Firstly, it is shown that the category…

A survey is given of results about coherence for categories with finite products and coproducts. For these results, which were published previously by the authors in several places, some formulations and proofs are here corrected, and…

We relativize the notion of a compact object in an abelian category with respect to a fixed subclass of objects. We show that the standard closure properties persist to hold in this case. Furthermore, we describe categorical and…

We introduce para-associative algebroids as vector bundles whose sections form a ternary algebra with a generalised form of associativity. We show that a necessary and sufficient condition for local triviality is the existence of a…

We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…

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 whether a class is closed under pure subobjects, pure…

Let $\Lambda = \left[\begin{array}{cc} A & 0 \\ M & B \end{array}\right] $ be an Artin algebra and $_BM_A$ a $B$-$A$-bimodule. We prove that there is a triangle equivalence $D_{sg}(\Lambda) \cong D_{sg}(A)\coprod D_{sg}(B)$ between the…

This work is an attempt towards a Morita theory for stable equivalences between self-injective algebras. More precisely, given two self-injective algebras A and B and an equivalence between their stable categories, consider the set S of…

We prove a constructive existence theorem for abelian envelopes of non-abelian monoidal categories. This establishes a new tool for the construction of tensor categories. As an example we obtain new proofs for the existence of several…