Nonabelian cohomology explained

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

• Web site: B. . Toën . Stacks and non-abelian cohomology . dead . https://web.archive.org/web/20140114023724/http://www.math.univ-montp2.fr/~toen/msri2002.pdf . January 14, 2014 .
• Book: Lurie, Jacob . . 1175.18001 . Annals of Mathematics Studies . 170 . Princeton, NJ . . 978-0-691-14049-0 . 2009 .