Let $\mathbf{H}$ be an (∞,1)-topos and $X \in \mathbf{H}$ an object. At least in nice situations the locally constant ∞-stacks on $X$, represented by morphisms $X \to LConst Core(\infty Grpd)$ are equivalently encoded by the adjunct morphism $\Pi(X) \to \infty Grpd$ out of the bare path ∞-groupoid. This morphism exhibits the monodromy of the locally constant ∞-stack.

Specifically, the restriction $\mathbf{B}\Omega_x \Pi(X) \hookrightarrow \Pi(X) \to \infty Grpd$ to the delooping$\mathbf{B}\Omega_x \Pi(X)$ of the loop space object$\Omega_x \Pi(X)$ at a chosen baspoint $x : {*} \to X$ is the monodromy action of loops based at $x \in X$ on the fiber of the locally constant $\infty$-stack over $x$.