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

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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 languageUnknown
Pages (from-to)3850-3877
JournalJournal of Algebra
Volume321
Issue number12
DOIs
Publication statusPublished - 1 Jan 2009

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