The Bredon cohomology, introduced by Glen E. Bredon, is a type of equivariant cohomology that is a contravariant functor from the category of G {\displaystyle G} -complexes with equivariant homotopy maps to the category of abelian groups together with the connecting homomorphism satisfying some conditions.
References Bredon, Glen E. (2006) [1967], Equivariant cohomology theories, Lecture Notes in Mathematics, vol. 34, Springer, ISBN 978-3-540-34973-0, MR 0214062 Illman, Sören (1973), "Equivariant singular homology and cohomology", Bulletin of the American Mathematical Society, 79: 188–192, doi:10.1090/S0002-9904-1973-13148-9, MR 0307220