After quite a few studying experiences (both alone and following a class, studying topology, algebra, analysis, measure theory, differential geometry) I have acquired a lot of notes that I have either written up by hand or into the computer (using mostly Lyx).
What always annoys me is that using a computer, the software I use knows nothing about how the different objects I'm creating relate to each other and about their interdependence. In the best case you could create hierarchy of chapter / section / subsection and paragraphs.
But after going on like this for quite a while and then finding myself looking at the old notes, I realize there must be a better way to navigate through this information.
Is there any kind of math-taking software where I can define objects of different type (the types could be: "primitive", "definition", "claim", "proof", "example", "counter example", "remark"), and each object would have a set of links, each link having itself a type ("relies_on", "is_a_proof_of", "is_a_counter_example_of", etc) and hopefully also tags that would put it in a certain field of math, like "#algebra" and "#finite_abelian_groups".
Then I could picture there would be many different ways to "query" this network, either searching by free text of something in particular and seeing how it fits in the whole, or looking up a proof to a theorem and being able to drill down to the most elementary level, or, for example, if you're trying to prove that a certain topological space is compact, you could query all the claims that end up with a compact space and see if any of their conditions pertain to your particular situation.
A very naive depiction of one visualization to a network, which includes only definitions, is shown in the picture below, where I imagine clicking on any box would display the corresponding definition, and maybe allow you to navigate to all the results that rely on it.
I am aware that there are proof assistants but they somehow seem to be more geared towards the construction of proofs rather to the organizing of the information into an expandable, searchable, indexable network.
Is there any existing software which is remotely similar to what I'm thinking about?