group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
Differential cobordism cohomology is the refinement to differential cohomology of cobordism cohomology theory.
By tensoring with a Landweber exact ring, this induces various other differential cohomology theories, such as differential elliptic cohomology.
A model for a multiplicative differential refinement of complex cobordism cohomology theory, the theory represented by the Thom spectrum is in