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How from a local system $\mathcal{F}$ with value in an R-module over a topological space $X$, can we associate a representation of $\pi_1(X)$?

More precisely, how does $\pi_1(x)$ act on the stalk $\mathcal{F}_x$ concretely? and why does it induce a representation?

I found the proof in the book of Szamuely "Galois groups and fundamental groups" page 51 Theorem 2.5.15, however it is not evident from me why the addition should be a map of $\pi_1(X)$-sets.

Tinhinane
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    Also, your tags mean that your question won't be found by many people. Something broader (like [tag:algebraic-topology]) would get you a wider audience. Hover over a tag with your mouse to see how many "watchers" it has: [tag:fundamental-groups] has 40, [tag:local-systems] has 1, but [tag:algebraic-topology] has 1.1k. – user1729 Jun 02 '21 at 11:28
  • Thank you for your advice. – Tinhinane Jun 02 '21 at 11:46
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    Your question is cryptic and impossible to answer by anybody not familiar with the specific proof given in Szamuely's book. The statement itself is also proven by Steenrod in "Topology of fiber bundles." The proof is a bit painful. – Moishe Kohan Jun 02 '21 at 13:11

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