Monodromy theorem

Stream: Is there code for X?

[Geoffrey Irving]

Do we have (a generalization of) the Monodromy theorem in complex analysis, saying that if a function can be analytically continued along any path in a simply connected domain, then the analytic continuation is path independent? I imagine there is an extremely general sheaf version of this theorem that people typically use nowadays, but I don't know enough category theory to know how to search for it.

[Ruben Van de Velde]

Not by that name, as far as I can tell

[Geoffrey Irving]

Yes, I did search for the name before asking. The problem is that the sheaf-theoretic generalization might be abstract enough to have an unrelated name.

[Geoffrey Irving]

I suppose the generalization might just be that (nice enough?) simply connected spaces have only trivial covering spaces.