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.
twisted Bredon cohomology (twisted ordinary equivariant cohomology)
Norman Steenrod, Homology With Local Coefficients, Annals of Mathematics, Second Series, Vol. 44, No. 4 (Oct., 1943), pp. 610-627 (jstor:1969099)
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)
Discussion of classification by fibrations of Eilenberg-MacLane spaces:
Yasumasa Hirashima, A note on cohomology with local coefficients, Osaka J. Math., Volume 16, Number 1 (1979), 219-231 (euclid:ojm/1200771839)
Paul Goerss, J. F. Jardine, p. 332 of: Simplicial homotopy theory, Progress in Mathematics, Birkhäuser (1999) Modern Birkhäuser Classics (2009) (doi:10.1007/978-3-0346-0189-4)
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)
Discussion of cohomology operations in twisted ordinary cohomology:
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