# nLab nonabelian sheaf cohomology

Nonabelian sheaf cohomology is a notion in the context of nonabelian cohomology:

Given an infinity-category-valued (pseudo)presheaf $\mathbf{A} : Spaces^{op} \to \infty-Cat$, its cohomology $H(-,\mathbf{A})$ is the $\infty$-category valued (pseudo)presheaf which assigns to each space the directed limit over all descent data:

$H(X, \mathbf{A}) := colim_{Y^\bullet \to X} Desc(Y^\bullet, \mathbf{A}) \,.$

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

# Remarks

Revised on April 28, 2009 19:34:08 by Toby Bartels (71.104.234.95)