nLab
nonabelian cocycle

A nonabelian cocycle is, generally, a cocycle in nonabelian cohomology.

This means usually that it is modeled in either of the following two ways:

  • a descent datum, i.e. an object in the category of descent data (sometimes briefly called a descent category);
  • an ω\omega-anafunctor.

Notice that for n2n\geq 2, descent data in a setup of strict nn-categories still form a strict (n+1)(n+1)-category, while nn-anafunctors form weak (n+1)(n+1)-category.

Revised on June 9, 2009 02:20:52 by Toby Bartels (71.104.230.172)