Postnikov towers, k-invariants and obstruction theory for dg categories

Gonçalo Jorge Trigo Neri Tabuada

doi:10.1016/j.jalgebra.2009.03.018

Postnikov towers, k-invariants and obstruction theory for dg categories

Gonçalo Jorge Trigo Neri Tabuada

DM - Departamento de Matemática

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

By inspiring ourselves in Drinfeld's DG quotient, we develop Postnikov towers, k-invariants and an obstruction theory for dg categories. As an application, we obtain the following 'rigiclification' theorem: let A be a homologically connective dg category and F-0 : B -> H-0(A) a dg functor to its homotopy category. If the inductive family {omega(n)(F-n)}n >= 0 of obstruction classes vanishes, then a lift F : B -> A for F-0 exists. (c) 2009 Elsevier Inc. All rights reserved.

Original language	Unknown
Pages (from-to)	3850-3877
Journal	Journal of Algebra
Volume	321
Issue number	12
DOIs	https://doi.org/10.1016/j.jalgebra.2009.03.018
Publication status	Published - 1 Jan 2009

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10.1016/j.jalgebra.2009.03.018

Cite this

@article{01aabe4dcc764aefa4afbe4190d673fc,

title = "Postnikov towers, k-invariants and obstruction theory for dg categories",

abstract = "By inspiring ourselves in Drinfeld's DG quotient, we develop Postnikov towers, k-invariants and an obstruction theory for dg categories. As an application, we obtain the following 'rigiclification' theorem: let A be a homologically connective dg category and F-0 : B -> H-0(A) a dg functor to its homotopy category. If the inductive family {omega(n)(F-n)}n >= 0 of obstruction classes vanishes, then a lift F : B -> A for F-0 exists. (c) 2009 Elsevier Inc. All rights reserved.",

keywords = "algebraic, spectra, Drinfeld's, Dg, DG, k-Invariants, ring, Non-commutative, homotopy-theory, Obstruction, quotient, Postnikov, geometry, category, theory, tower",

author = "Tabuada, {Gon{\c c}alo Jorge Trigo Neri}",

year = "2009",

month = jan,

day = "1",

doi = "10.1016/j.jalgebra.2009.03.018",

language = "Unknown",

volume = "321",

pages = "3850--3877",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Elsevier Science B.V., Amsterdam.",

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TY - JOUR

T1 - Postnikov towers, k-invariants and obstruction theory for dg categories

AU - Tabuada, Gonçalo Jorge Trigo Neri

PY - 2009/1/1

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N2 - By inspiring ourselves in Drinfeld's DG quotient, we develop Postnikov towers, k-invariants and an obstruction theory for dg categories. As an application, we obtain the following 'rigiclification' theorem: let A be a homologically connective dg category and F-0 : B -> H-0(A) a dg functor to its homotopy category. If the inductive family {omega(n)(F-n)}n >= 0 of obstruction classes vanishes, then a lift F : B -> A for F-0 exists. (c) 2009 Elsevier Inc. All rights reserved.

AB - By inspiring ourselves in Drinfeld's DG quotient, we develop Postnikov towers, k-invariants and an obstruction theory for dg categories. As an application, we obtain the following 'rigiclification' theorem: let A be a homologically connective dg category and F-0 : B -> H-0(A) a dg functor to its homotopy category. If the inductive family {omega(n)(F-n)}n >= 0 of obstruction classes vanishes, then a lift F : B -> A for F-0 exists. (c) 2009 Elsevier Inc. All rights reserved.

KW - algebraic

KW - spectra

KW - Drinfeld's

KW - Dg

KW - DG

KW - k-Invariants

KW - ring

KW - Non-commutative

KW - homotopy-theory

KW - Obstruction

KW - quotient

KW - Postnikov

KW - geometry

KW - category

KW - theory

KW - tower

U2 - 10.1016/j.jalgebra.2009.03.018

DO - 10.1016/j.jalgebra.2009.03.018

M3 - Article

VL - 321

SP - 3850

EP - 3877

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 12

ER -