Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems [unknown]

Ronald Brown
2004 Galois Theory, Hopf Algebras, and Semiabelian Categories   unpublished
We outline the main features of the definitions and applications of crossed complexes and cubical ωgroupoids with connections. These give forms of higher homotopy groupoids, and new views of basic algebraic topology and the cohomology of groups, with the ability to obtain some non commutative results and compute some homotopy types. * This is an extended account of a lecture given at the meeting on 'Categorical Structures for Descent, Galois Theory, Hopf algebras and semiabelian categories ', Fields Institute, September 23-28, 2002.
doi:10.1090/fic/043/05 fatcat:fgnoiqw475fijaywww2q2vxtje