Given your favorite field $k$, we can build its groupoid of algebraic closures in the obvious way: Look at the category of all possible algebraic closures with field isomorphisms as the arrows.
This is interesting, because most topics in galois theory aren't functorial: we have to make a bunch of arbitrary choices (picking a root, etc.). Of course, we can "canonical-ify" this construction in the usual way -- just look at all choices at once. This feels like something that people would have thought about, but I'm struggling to find references for "elementary" galois theory done with groupoid machinery. Googling around it seems people are mainly talking about the absolute galois group of $\mathbb{Q}$ (a famously difficult object). This is interesting, but I would love to cut my teeth on something a bit simpler.
With that in mind, does anyone know of references for galois theory with groupoids, but pitched at a graduate student level rather than a research level? In particular, I would love to see splitting fields, finite galois extensions, etc. treated (if more advanced topics are treated, that's great too. But I would like to start with something I'm more familiar with).
Thanks in advance! ^_^