In mathematics, a nonabelian cohomology is any cohomology with coefficients in a nonabelian group, a sheaf of nonabelian groups or even in a topological space. If homology is thought of as the abelianization of homotopy (cf. Hurewicz theorem), then the nonabelian cohomology may be thought of as a dual of homotopy groups.
Nonabelian Poincaré duality
See: Nonabelian Poincare Duality (Lecture 8)
See also Stacks Group cohomology
References Toën, B. "Stacks and non-abelian cohomology" (PDF). Archived from the original (PDF) on January 14, 2014. Lurie, Jacob (2009). Higher Topos Theory. Annals of Mathematics Studies. Vol. 170. Princeton, NJ: Princeton University Press. ISBN 978-0-691-14049-0. Zbl 1175.18001.