We construct local-to-global spectral sequences for the cohomology of a diagram, which compute the cohomology of the full diagram in terms of smaller pieces. These are motivated by the obstruction theory of D. Blanc et al. [D. Blanc, M.W. Johnson, J.M. Turner, On realizing diagrams of Π-algebras, Algebraic Geom. Topol. 6 (2006) 763-807] for realizing a diagram of Π-algebras, but are valid in quite general algebraic settings.
Bibliographical noteFunding Information:
We would like to thank the referee for his or her comments. This research was supported by BSF grant 2006039; the third author was also supported by NSF grant DMS-0206647 and a Calvin Research Fellowship (SDG).
ASJC Scopus subject areas
- Algebra and Number Theory