Title: Local-to-global spectral sequences for the cohomology of diagrams Authors: David Blanc, Mark W. Johnson, and James M. Turner E-mail: blanc@math.haifa.ac.il, mwj3@psu.edu, jturner@calvin.edu Address: Department of Mathematics, University of Haifa, 31905 Haifa, Israel Department of Mathematics, Penn State Altoona, Altoona, PA 16601, USA Department of Mathematics, Calvin College, Grand Rapids, MI 49546, USA arXiv:0802.4096 Abstract: The cohomology of diagrams arises in various areas of mathematics, such as deformation theory, classifying diagrams of groups, and in homotopy theory, in the context of the rectification of homotopy-commutative diagrams, and thus in the study of higher homotopy and cohomology operations. For this purpose we construct ``local-to-global'' spectral sequences for the cohomology of a diagram, which can be used to compute the cohomology of the full diagram in terms of smaller pieces. We also explain why such a local-to-global approach is relevant to higher operations.