Comparing cohomology obstructions

Hans Joachim Baues, David Blanc

Research output: Contribution to journalArticlepeer-review


We show that three different kinds of cohomologies - Baues-Wirsching cohomology, the (S*,O)-cohomology of Dwyer and Kan, and the André-Quillen cohomology of a. Π-algebra - are isomorphic, under certain assumptions. This is then used to identify the cohomological obstructions in three general approaches to realizability problems: the track category version of Baues and Wirsching, the diagram rectifications of Dwyer, Kan, and Smith, and the Π-algebra realization of Dwyer, Kan, and Stover. Our main tool in this identification is the notion of a mapping algebra: a simplicially enriched version of an algebra over a theory.

Original languageEnglish
Pages (from-to)1420-1439
Number of pages20
JournalJournal of Pure and Applied Algebra
Issue number6
StatePublished - Jun 2011

Bibliographical note

Funding Information:
We thank the referee for his or her comments. The second author would like to thank the Max-Planck-Institut für Mathematik for hospitality while this research was carried out. He would also like to thank Bernard Badzioch, Wojtek Dorabiała, Mark Johnson, and Jim Turner for many useful discussions.


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ASJC Scopus subject areas

  • Algebra and Number Theory


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