  Standard results from non-abelian cohomology theory specialize to a theory of
torsors and stacks for cosimplicial groupoids. The space of global sections of
the stack completion of a cosimplicial groupoid $G$ is weakly equivalent to the
Bousfield-Kan total complex of $BG$ for all cosimplicial groupoids $G$. The
$k$-invariants for the Postnikov tower of a cosimplicial space $X$ are
naturally elements of stack cohomology for the stack associated to the
fundamental groupoid $\pi(X)$ of $X$. Cocycle-theoretic ideas and techniques
are used throughout the paper.
