# nLab nonabelian cosheaf homotopy

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

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

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

Here the limit is over all hypercovers of $X$.

# Remarks

Revised on April 28, 2009 19:34:17 by Toby Bartels (71.104.234.95)