| dbp:proof
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- Take local system and a loop at x. It's easy to show that any local system on is constant. For instance, is constant. This gives an isomorphism , i.e. between and itself.
Conversely, given a homomorphism , consider the constant sheaf on the universal cover of X. The deck-transform-invariant sections of gives a local system on X. Similarly, the deck-transform-ρ-equivariant sections give another local system on X: for a small enough open set U, it is defined as
:
where is the universal covering. (en)
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