nLab
local coefficient bundle

Idea

In the context of twisted cohomology a cocycle on a space $X$ with coefficients in a coefficient object $V$ is not quite a direct morphism $X\to V$ as in ordinary $G$-cohomology, but is instead a section of a $V$-fiber ∞-bundle $E\to X$ over $X$. This is called the local coefficient bundle for the given twisted cohomology. Its class $[E]\in H^1(X,\mathrm{Aut}(V))$ is the twist.

Related concepts

• twisted cohomology, local system of coefficients

• twisted infinity-bundle