Comparing cohomology obstructions |
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Authors: | Hans-Joachim Baues |
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Institution: | a Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germanyb Department of Mathematics, University of Haifa, 31905 Haifa, Israel |
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Abstract: | 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 aΠ-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. |
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Keywords: | Primary 55S35 Secondary 55Q05 18G55 55T25 |
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