How to check path in nested sets?

Question

SQL

There is a nested sets tree of categories that contains a slug
, it looks something like this:

(это все slug)
- one
- - two
- - - three
- - three
- two

That is, url at different levels of nesting can be repeated, because the path is still different.
I can’t figure out how to check if the path to the category is correct?
/one/two/three
How to get the element three given the full path without making a separate request for each section?
UPD I could get the last element (three) and check its parents, but there can be several categories with the three slug, at the same nesting level, but with different parents