English
Related papers

Related papers: A note on stable recollements

200 papers

Simple-minded systems in stable module categories are defined by orthogonality and generating properties so that the images of the simple modules under a stable equivalence form such a system. Simple-minded systems are shown to be invariant…

Representation Theory · Mathematics 2010-09-09 Steffen Koenig , Yuming Liu

We prove that, in a triangulated category with combinatorial models, every localizing subcategory is coreflective and every colocalizing subcategory is reflective if a certain large-cardinal axiom (Vopenka's principle) is assumed true. It…

Category Theory · Mathematics 2013-12-10 Carles Casacuberta , Javier J. Gutiérrez , Jiří Rosický

We prove that a large family of graphs which are decomposable with respect to the modular decomposition can be reconstructed from their collection of vertex-deleted subgraphs.

Combinatorics · Mathematics 2012-02-28 Robert Brignall , Nicholas Georgiou , Robert J. Waters

We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…

Logic in Computer Science · Computer Science 2023-03-29 Vincent van Oostrom

Various concerns suggest looking for internal co-categories in categories with strong logical structure. It turns out that in any coherent category, all co-categories are co-equivalence relations.

Category Theory · Mathematics 2014-11-21 Peter LeFanu Lumsdaine

Eventual consistency of replicated data supports concurrent updates, reduces latency and improves fault tolerance, but forgoes strong consistency. Accordingly, several cloud computing platforms implement eventually-consistent data types.…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-10-15 Annette Bieniusa , Marek Zawirski , Nuno Preguiça , Marc Shapiro , Carlos Baquero , Valter Balegas , Sérgio Duarte

In this note, we define a recollement of additive categories, and prove that such a recollement can induce a recollement of their quotient categories. As an application, we get a recollement of quotient triangulated categories induced by…

Representation Theory · Mathematics 2015-02-03 Minxiong Wang , Zengqiang Lin

In this paper, firstly, we mainly study the relationship of balanced pairs among three Abelian categories in a recollement. As an application of admissible balanced pairs, we introduce the notion of the relative tilting modules, and give a…

Category Theory · Mathematics 2022-05-20 Peiyu Zhang , Dajun Liu , Jiaqun Wei

By a theorem due to the first author, the bounded derived category of a finite-dimensional algebra over a field embeds fully faithfully into the stable category over its repetitive algebra. This embedding is an equivalence iff the algebra…

Representation Theory · Mathematics 2007-05-23 Dieter Happel , Bernhard Keller , Idun Reiten

We provide a technique to glue simple-minded collections along a recollement of Hom-finite Krull-Schmidt triangulated categories over a field. This gluing technique for simple-minded collections is shown to be compatible with those for…

Representation Theory · Mathematics 2024-02-19 Yongliang Sun , Yaohua Zhang

We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras, or appropriate subreducts, of the resulting structure. Starting from the 1-sum construction…

Logic · Mathematics 2023-06-02 Nick Galatos , Sara Ugolini

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…

Logic · Mathematics 2023-02-17 Saharon Shelah , Alexander Usvyatsov

These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 Nicolas Tabareau , Jean-Jacques Slotine

We study when the stable category of an abelian category modulo a full additive subcategory is balanced and, in case the subcategory is functorially finite, we study a weak version of balance. Precise necessary and sufficient conditions are…

Category Theory · Mathematics 2010-10-05 Pedro Nicolas , Manuel Saorin

Coherent analyses of experimental results from LHC and ILC will allow us to draw a comprehensive and precise picture of the supersymmetric particle sector. Based on this platform the fundamental supersymmetric theory can be reconstructed at…

High Energy Physics - Phenomenology · Physics 2007-05-23 G. A. Blair , A. Freitas , H. -U. Martyn , G. Polesello , W. Porod , P. M. Zerwas

We prove basic facts about reflexivity in derived categories over noetherian schemes; and about related notions such as semidualizing complexes, invertible complexes, and Gorenstein-perfect maps. Also, we study a notion of rigidity with…

Algebraic Geometry · Mathematics 2010-01-21 Luchezar L. Avramov , Srikanth B. Iyengar , Joseph Lipman

We propose a framework for model-theoretic stability and simplicity in an approximate first-order setting and generalize some classical results.

Logic · Mathematics 2026-04-27 Alexander Burka

For an exact category having enough projective objects, we establish a bijection between thick subcategories containing the projective objects and thick subcategories of the stable derived category. Using this bijection we classify thick…

Category Theory · Mathematics 2015-01-14 Henning Krause , Greg Stevenson

Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…

Logic in Computer Science · Computer Science 2017-05-30 Brendan Fong , Fabio Zanasi

Let $A={\rm \mathbb{k}}Q/\mathcal{I}$ be a gentle algebra. We provide a bijection between non-projective indecomposable Gorenstein projective modules over $A$ and special recollements induced by an arrow $a$ on any full-relational oriented…

Representation Theory · Mathematics 2024-10-01 Yu-Zhe Liu , Dajun Liu , Xin Ma