The basic problem is that to get to the objects you mention here is at least 3 or 4 years of full-time study away from the kind of math people learn for a typical college degree in science or engineering. If you really want to understand them, to make your "digging" efficient you should probably just get a pure math degree, but setting aside several years to satisfy occasional curiosity is not feasible for most people for various reasons.

One unfortunate feature of published pure math research is that often the ideas are quite accessible and straightforward and don't really require special abstractions or terminology, but those get used anyway because for someone who already has a math PhD it saves a bit of effort.