CanadaPlus , 7 hours ago (edited 3 hours ago)

Calm down, everyone. Brackets form a tree structure, and can be represented by a free magma, while strings with concatenation are equivalent to a free monoid. You’re essentially asking for the two respective common involutory operations to be connected by this map, just because they’re involutory, which put that way is a wild guess at best. In fact, reversing this string produces something outside the range of the map entirely, which is injective and so can’t be surjective for combinatorical reasons.

… Yeah I might be the only person that finds that useful.