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Deformation of dg categories

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], … WebWe introduce a homotopy 2-category structure on the collection of dg-categories, dg-functors, and their derived transformations. This construction provides for a conceptual …

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Web1.2. 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 ... Webfer it to model category structures on dg Lie algebras and commutative dg algebras; (2)formulate a variant of the nerve construction that produces an 1-category from an ordinary model category. This is how we will de ne the underlying 1-categories (Lie, commutative algebras) that make up our derived enhancement of deformation theory. safir website https://acausc.com

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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 http://library.msri.org/books/Book62/files/kajiura.pdf 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 they\\u0027re xe

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Category:Deformation theory of objects in homotopy and derived categories …

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Deformation of dg categories

HOMOTOPY THEORY OF DG CATEGORIES VIA LOCALIZING …

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). WebDec 23, 2024 · Edit social preview. This paper is a sequel to "t-structures and twisted complexes on derived injectives" by the same authors. We develop the foundations of …

Deformation of dg categories

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http://www.numdam.org/item/10.1016/j.ansens.2007.05.001.pdf WebOct 1, 2009 · Namely, for a DG module E over a DG category we define four deformation functors Defh(E), coDefh(E), Def(E), coDef(E). The first two functors describe the …

WebUsing localizing pairs and Drinfeld's dg quotient we construct a new Quillen model for the homotopy theory of dg categories. We prove that, in contrast with the original model, … 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 …

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 WebV.Drinfeld, DG quotients of DG categories. E-preprint. B.Keller, Introduction to A-infinity algebras E-preprint. K.Lefevre-Hasegawa, Sur les A-infini categories. from author's page. M.Kontsevich's course on deformation theory. Course notes in PostScript. V.Ginzburg, Lectures on noncommutative geometry. E-preprint.

WebMay 15, 2024 · In particular, the DGLA completely determines a derived deformation functor. Since the ∞ -categories of connective Artinian local E ∞ -algebras and of cdgas as above are equivalent, this suffices to give a functor in Lurie's setup. Beware that the derived deformation functor is highly dependent on the choice of L, and is not determined by ...

WebOct 1, 2009 · This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG … they\u0027re xdWebApr 12, 2024 · To determine and compare the measurement uncertainty of different geological-geotechnical testing methods, numerous test locations were selected in a hard rock quarry. Measurements were carried out along two vertical measurement lines perpendicular to the mining levels of an existing exploration. Along these lines, the rock … they\u0027re xhWebAn example of this philosophy is the deformation theory of a compact complex manifold: It is "controlled" by the Kodaira-Spencer dg Lie algebra: holomorphic vector fields tensor Dolbeault complex, with differential induced by del-bar on the Dolbeault complex, and Lie bracket induced by Lie bracket on the vector fields (I think also take wedge ... they\\u0027re xi