nonabelian cosheaf homotopy

Nonabelian cosheaf homotopy is a notion in the context of nonabelian cohomology:

Given an infinity-category-valued (pseudo)copresheaf B:SpacesCat\mathbf{B} : Spaces \to \infty-Cat, its homotopy π(,B)\pi(-,\mathbf{B}) is the \infty-category valued (pseudo)copresheaf which assigns to each space the limit over all codescent data:

π(X,B):=lim Y XCodesc(Y ,B). \pi(X, \mathbf{B}) := lim_{Y^\bullet \to X} Codesc(Y^\bullet, \mathbf{B}) \,.

Here the limit is over all hypercovers of XX.


Revised on April 28, 2009 19:34:17 by Toby Bartels (