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This question about the difference between holonomy and monodromy has an interesting answer by Ronnie Brown.

An excerpt:

So holonomy comes out as a kind of right adjoint, and monodromy as a kind of left adjoint, which explains one difference.

I tried looking into the suggested references, but I failed to see the big picture.

Question. What is the correct setting for the excerpt? Precisely how are the holonomy and monodromy functors defined, and what are they adjoint to?

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  • What I can guess from a fast reading of https://arxiv.org/pdf/math/0110064.pdf is that holonomy and monodromy are functors from locally Lie groupoids to Lie groupoids and that the functor they are adjoint to is restriction to a nhbhd of the identity: see theorem 2.1 in the above ref and Theorem B of https://groupoids.org.uk/pdffiles/brownmucuk1CTGDC_1995__36_4_345_0.pdf – Nicola Ciccoli Nov 17 '19 at 11:55
  • @NicolaCiccoli thank you for your comment.. That was useful... :) – Praphulla Koushik Nov 17 '19 at 14:46

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