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?