Reading through Wikipedia, I saw this:
It has been shown that the Merkle–Damgård construction, as used by SHA-2, is collapsing and, by consequence, quantum collision-resistant, but for the sponge construction used by SHA-3, the authors provide proofs only for the case that the block function f is not efficiently invertible; Keccak-f, however, is efficiently invertible, and so their proof does not apply.
What does "efficiently invertible" mean in this case? It isn't reversible (as in decryption), so what else could that mean?
Why is Keccak invertible? Is it by design or did they not bother as it's not important?