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Related papers: Duality for distributive space

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We introduce a general framework for generating dualities between categories of partial orders and categories of ordered Stone spaces; we recover in particular the classical Priestley duality for distributive lattices and establish several…

Category Theory · Mathematics 2012-03-14 Olivia Caramello

Working in the framework of $(T, V)$-categories, for a symmetric monoidal closed category $V$ and a (not necessarily cartesian) monad $T$, we present a common account to the study of ordered compact Hausdorff spaces and stably compact…

Category Theory · Mathematics 2014-10-27 Dimitri Chikhladze , Maria Manuel Clementino , Dirk Hofmann

The goal of this papers is to extending to the complex analytic framework the relative Kleiman duality for quasi coherent sheaves. Precisely, he show that for any flat,locally projectivea and finitely presented morphism of schemes…

Algebraic Geometry · Mathematics 2024-06-17 Mohamed Kaddar

We prove coherence theorems for dualizable objects in monoidal bicategories and for fully dualizable objects in symmetric monoidal bicategories, describing coherent dual pairs and coherent fully dual pairs. These are property-like…

Algebraic Topology · Mathematics 2014-11-26 Piotr Pstrągowski

We discover a class of projective self-dual algebraic varieties. Namely, we consider actions of isotropy groups of complex symmetric spaces on the projectivized nilpotent varieties of isotropy modules. For them, we classify all orbit…

Analysis of PDEs · Mathematics 2007-05-23 Vladimir L. Popov , Evgueni A. Tevelev

It is known since the late 1960's that the dual of the category of compact Hausdorff spaces and continuous maps is a variety -- not finitary, but bounded by $\aleph_1$. In this note we show that the dual of the category of partially ordered…

Category Theory · Mathematics 2017-06-19 Dirk Hofmann , Renato Neves , Pedro Nora

In this paper we prove a duality for constructible sheaves on conically smooth stratified spaces. Here we consider sheaves with values in a stable and bicomplete $\infty$-category equipped with a closed symmetric monoidal structure, and in…

Algebraic Topology · Mathematics 2023-12-04 Marco Volpe

We demonstrate equivalence between two definitions of lower finite highest weight categories. We also show that, in the presence of a duality, a lower finite highest weight structure on a category is unique. Finally, we give a new proof for…

Representation Theory · Mathematics 2020-05-20 Kevin Coulembier

Huang, Lepowsky and Zhang have developed a module theory for vertex operator algebras that endows suitably chosen module categories with the structure of braided monoidal categories. Included in the theory is a functor which assigns to…

Quantum Algebra · Mathematics 2021-09-08 Robert Allen , Simon Lentner , Christoph Schweigert , Simon Wood

This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…

General Topology · Mathematics 2026-03-25 Masaki Taho

It has long been known in universal algebra that any distributive sublattice of congruences of an algebra which consists entirely of commuting congruences yields a sheaf representation of the algebra. In this paper we provide a…

Rings and Algebras · Mathematics 2019-04-12 M. Gehrke , S. J. v. Gool

Grothendieck-Verdier duality is a powerful and ubiquitous structure on monoidal categories, which generalises the notion of rigidity. Hopf algebroids are a generalisation of Hopf algebras, to a non-commutative base ring. Just as the…

Quantum Algebra · Mathematics 2024-02-12 Robert Allen

In this paper, we provide an alternative description of the duality result for distributive lattices and coherent locales using ultraposet. In particular, we show that there are fully faithful embeddings from the opposite of the category of…

Category Theory · Mathematics 2023-04-24 Lingyuan Ye

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

Algebraic Topology · Mathematics 2016-12-16 Sinan Yalin

This paper has two purposes. The first is to extend the theory of linearly distributive categories by considering the structures that emerge in a special case: the normal duoidal category $(\mathsf{Poly} ,\mathcal{y}, \otimes, \triangleleft…

Category Theory · Mathematics 2024-07-03 David I. Spivak , Priyaa Varshinee Srinivasan

It is well-known that small categories have equivalent descriptions as partial monoids. We provide a formulation of partial monoid and partial monoid homomorphism involving $s$ and $t$ instead of identities and then following a recent…

Category Theory · Mathematics 2015-03-02 Rachel A. D. Martins

The paper is devoted to a categorical study of the category of probabilistic metric spaces. The study is based on an isomorphic description of the category of probabilistic metric spaces. The isomorphic description was obtained in [3] and…

General Topology · Mathematics 2026-04-02 Eva Colebunders , Robert Lowen

In this article, we prove that there is a canonical Verdier self-dual intersection space sheaf complex for the middle perversity on Witt spaces that admit compatible trivializations for their link bundles, for example toric varieties. If…

Algebraic Geometry · Mathematics 2020-06-02 M. Agustin , J. T. Essig , J. Fernandez de Bobadilla

In this note we identify two complex structures (one is given by algebraic geometry, the other by gauge theory) on the set of isomorphism classes of holomorphic bundles with section on a given compact complex manifold. In the case of line…

Algebraic Geometry · Mathematics 2007-05-23 Siegmund Kosarew , Paul Lupascu

Quantum LDPC codes have attracted intense interest due to their advantageous properties for realizing efficient fault-tolerant quantum computing. In particular, sheaf codes represent a novel framework that encompasses all well-known good…

Quantum Physics · Physics 2026-01-01 Yiming Li , Zimu Li , Zi-Wen Liu , Quynh T. Nguyen