Reciprocal is its own inverse, so the reciprocal of a/b/c and d/e/f can't both be "..".
The closest you could come is an anti-path, where if you are at a/b/c, you could have c'/b'/a' that when combined together produced the root path of both these things. You could then have things like b'/a, which represents "rise up to the previous directory, which is named 'b', and descend into a" where the reciprocal is a'/b. I'm done fiddling with this for now, but it's possible you could work this into a sensible scheme with some concept of "reciprocal". It's useless in practice because who wants a .. operator that asserts the name of the directory it is rising from? (And presumably, what, errors if it isn't right? Refuses to rise like .. does at the root?)
However since Fractional instances also have to be Num instances [1], and there's no practical way to fill in most of those, it's not going to get you very far. And the Fractional requirement of fromRational, while you can try to write something that turns a Rational (which in Haskell is specifically two Integers being used as a ratio) into a path, it's going to be very silly.
[1]: https://hackage.haskell.org/package/base-4.12.0.0/docs/Prelu...