TITLE: Category-theoretic characterization of locally constant sheaves
QUESTION [7 upvotes]: Let's consider $X$ a (locally connected) topological space and $\mathcal{Sh}(X)$ the topos of sheaves over $X$.
If you see sheaves as étale spaces, locally constants sheaves correspond to covering spaces.
Is there an internal (topos-theoretic) characterization of the locally constant sheaves?
I've searched in Sheaves in Geometry and Logic, but I haven't found anything, and in the nLab there seems to be something but I do not understand it (and it does not really look like an internal characterization).

REPLY [3 votes]: One can talk about locally constant objects in a topos and these lead to covering spaces for sheaves on a space. Finite covers are already in SGA or the first Johnstone topos book. Barr and Diaconescu On locally simply connected toposes and their fundamental groups begins the modern theory. See papers by Bunge for more modern formulations.