Trivial bundle is a good example for many things but you don't see a lot about it for some reason

@Slereah what do you mean? The problem with the trivial bundle as an example is that you don't really need any of the "bundle techniques" - it has a single trivializing chart, it always has global sections, etc.

Yes, but it's a good pedagogical example for many concepts!

things you can construct explicitely and simple to solve usually

@Slereah now I’m curious where the commutative diagram is from

I think no two books use the same symbol for the parallel propagator

$g$, $P$, $\tau$, $\mathrm{tra}$

@Semiclassical interestingly, Google's image search is completely useless because it shows a bunch of drawings of cubic lattices as related images - it doesn't seem to pick up on the significance of the labels