An entry in Fortnightly Topic Challenge #42: Wordless Connecting Walls-- wait, what?
This is a Shingoki puzzle. The rules (paraphrased from puzzle-shingoki.com) are as follows:
The aim is to form a single loop without crossing or branching paths.
For the loop created to be valid, it must pass through all of the given circles. The circles also have their own rules:
- A line must go straight through a white circle.
- A line must turn 90 degrees upon a black circle.
Lastly, the number in the circle indicates the total length of the lines going out from that circle (disregarding other circles positioned on those lines). In our case, the grid we have has dimensions of 10 units by 10 units.
For now I will choose not to say all two groups that have been identified correctly, but just one of them: yes, the final answer looks like a letter 'm'. Keep looking as well; the intended categories are simpler than those speculated by @Deusovi.
Yes, the final answer is a Greek letter. And in fact, knowing these two hints would probably already be sufficient to find the final symbol and then just work backward from there for the remaining categories. Nevertheless, I will say that there is also one aspect characterizing Unicode related to one of the categories.