nLab
nonabelian sheaf cohomology

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

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

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

Here the colimit is over all hypercovers of XX.

Remarks

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