Journal of Pure and Applied Algebra
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. © 2008 Elsevier B.V. All rights reserved.
Blanc, David; Johnson, Mark W.; and Turner, James M., "Local-to-global spectral sequences for the cohomology of diagrams" (2009). University Faculty Publications and Creative Works. 269.