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.
|Number of pages||20|
|Journal||Journal of Pure and Applied Algebra|
|State||Published - Jun 2011|
Bibliographical noteFunding 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.
ASJC Scopus subject areas
- Algebra and Number Theory