For sufficiently nice topological spaces $X$ (e.g., locally connected for the last two categories to be equivalent, and semilocally simply connected and locally path-connected for all three to be equivalent), the following three categories are equivalent:

* Functors from the fundamental groupoid of $X$ to the category of sets;

* Covering spaces over $X$;

* Locally constant sheaves of sets on $X$.

This is an extremely primitive baby version of the Riemann–Hilbert correspondence.

References specifically for this elementary case are sparse,
but there is an [extensive discussion on locally constant sheaves](https://golem.ph.utexas.edu/category/2010/11/locally_constant_sheaves.html) at the nCafé.