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Deformation of dg categories

Webinvolved dg category of “right quasi-representable” bimodules (see Remark 5.1), when using the model Lp it is enough to derive its natural internal Hom-functor (see Defini-tion 5.2) which only makes use of dg categories of dg functors. We remind the reader that the construction of the internal Hom-objects in Hmo was the main difficulty in Web3.2 DG -Modules 72 3.3 DG Rings and Modules 74 3.4 DG Categories 78 3.5 DG Functors 80 3.6 Complexes in Abelian Categories 82 3.7 The Long Exact Cohomology Sequence 84 3.8 The DG Category C (A; M) 90 3.9 Contravariant DG Functors 94 4 Translations and Standard Triangles 101 4.1 The Translation Functor 101 4.2 The Standard Triangle of a …

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WebApr 30, 2024 · Flexible multifunctional sensors represent a significant branch of the next generation of flexible electronics, exhibiting great potential for application in smart wear, human–computer interaction, and soft robotics [1,2,3,4,5,6,7,8].Numerous types of pressure sensors already exist, such as capacitive inductive [9,10], piezoelectric ceramic [11,12], … Webdeformation from P2 blown up in two different points to P2 blown up along a subscheme of degree 2 supported at one point. 2. Enhanced triangulated categories ... A DG category C is ordered if there exists a partial order < on the set of objects such that C(A, B) — 0 for B -< A. It is finite if the set of objects of C is finite and molly ann beitner https://rodamascrane.com

On some deformations of Fukaya categories - MSRI

WebIn this Note, for the future purposes of relative formal derived deformation theory and of derived coisotropic structures, we prove the existence of a model structure on the category of dg-Lie algebroids over a cochain differential non-positively graded commutative algebra over a commutative base ring k of characteristic 0. Full PDF Webof categories between derived categories on the noncommutative complex torus and on a holomorphic gerbe on the dual complex torus. Contents 1. Introduction 2 2. The quasi-perfect category of modules over a di erential graded algebra 4 2.1. Review of the perfect DG category of a curved DGA 4 2.2. The Quasi-perfect category 6 2.3. DG … WebSep 23, 2024 · via the deformation theory [47, 53] of dg categories; see Remark 1 0.6 (2). The proof of Theor em A is divided into two steps. We first introduce the singular mollyann brodie

T-STRUCTURES ON DG-CATEGORIES AND DERIVED …

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Deformation of dg categories

Introduction DG categories - Harvard University

Web1 day ago · The deformation behavior of Mg-14Gd-0.5Zr (wt.%) was investigated via uniaxial compression tests at the temperature range of 375-500 ℃ and strain rate of 0.001-10 s-1.The constitutive equation was calculated to describe the flow stress behavior, and the processing maps were constructed using true stress-strain data through the Dynamic … WebOct 1, 2009 · We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module E over a DG category we define four deformation functors Def h ( E), coDef h ( E), Def ( E), coDef ( E).

Deformation of dg categories

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Web1.2. Hochschild complex and dg-Lie algebra 2 1.3. Deformation quantization of Poisson manifolds 5 2. Kontsevich’s formality theorem 8 1. Deformation theory 1.1. Deformation of associative algebras. Fix a eld kof characteristic zero. Let Abe an associative algebra. A formal deformation of Ais an associative kJ~K-algebra structure WebWe develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module E over a DG category we define four deformation functors Def h (E) , coDef h (E) , Def(E) , coDef(E). (Show Context) Citation Context (Corollary 15.15).

Webis based on the deformation of the standard toric generalized special La-grangian torus fibration of the large complex limit X0. In this paper, we will deal with the region near the smooth top dimensional torus fibres of X0 and its mirror dual situation: the region near the 0-dimensional fibres of X0. 1 Introduction Let (X,ω Web2.2 Approximation of formal moduli and loop spaces. As explained above, the deformation functor of a linear $\infty$-category over a field does not in general satisfy the derived Schlessinger conditions, but turns out to be rather close to satisfy them.Many examples of deformation functors of some algebro-geometric objects behave similarly.

WebMar 20, 2011 · This is the third paper in a series. In Part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show … WebAnthony Blanc (MPIM Bonn) On the deformation theory of dg-categories October 21st, 2015 3 / 20. Let k be a eld and B 0 an associative k-algebra. Let A be a commutative …

WebNov 23, 2024 · We prove the equivalence of the deformation theory for a higher dimensional Calabi--Yau manifold and that for its dg category of perfect complexes by giving a natural isomorphism of the...

WebFeb 8, 2012 · This paper is the first part of a project aimed at understanding deformations of triangulated categories, and more precisely their dg and A infinity models, and applying the resulting theory to... molly ann bishopWeb1.2. The 2-category of DG categories. We’d like to view the totality of DG categories as an (1;2)-category in 2 ways, denoted DGCat cont and DGCat, respectively, where in both cases the objects are DG categories, and the 1-morphisms are Funct cont(C 1;C 2) and Funct(C 1;C 2); respectively. For the most part, however, we’ll be working with ... molly ann brownWebThe homotopy theory of dg-categories and derived Morita theory EN English Deutsch Français Español Português Italiano Român Nederlands Latina Dansk Svenska Norsk Magyar Bahasa Indonesia Türkçe Suomi Latvian … molly ann brown fox newshttp://library.msri.org/books/Book62/files/kajiura.pdf mollyannbergman gmail.comWebKontsevich has been at least implicitly talking about deformations of categories since at least 1994, in the original paper introducing homological mirror symmetry. The idea (or … molly ann brook njmolly ann curleyWebJan 1, 2024 · Standard examples of dg manifolds are: (1) Lie algebras — Given a finite-dimensional Lie algebra g, we write g [ 1] to denote the dg manifold having C ∞ ( g [ 1]) = ∧ • g ∨ as its algebra of functions and the Chevalley–Eilenberg differential Q = d CE as its homological vector field. molly ann clymer od