group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
The twisted cohomology version of ordinary cohomology.
Norman Steenrod, Homology With Local Coefficients, Annals of Mathematics, Second Series, Vol. 44, No. 4 (Oct., 1943), pp. 610-627 (jstor:1969099)
M. Bullejos, E. Faro, M. A. García-Muñoz, Homotopy colimits and cohomology with local coefficients, Cahiers de Topologie et Géométrie Différentielle Catégoriques, 44 no. 1 (2003), p. 63-80 (numdam:CTGDC_2003__44_1_63_0)
Daniel Freed, Michael Hopkins, Constantin Teleman, Section 2 of: Consistent Orientation of Moduli Spaces (arXiv:0711.1909), chapter XIX, pages 395-419 in: Oscar Garcia-Prada, Jean Pierre Bourguignon, Simon Salamon (eds.) The Many Facets of Geometry: A Tribute to Nigel Hitchin, Oxford University Press 2010 (doi:10.1093/acprof:oso/9780199534920.001.0001)
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