Ask HN: What happens when someone copies an NFT onto another blockhain?

Let's say I'm the owner of the nyan cat NFT (I'm not). Is there anything that prevents someone from duplicating the nyan cat and putting it on another blockchain? If not, does the uniqueness of my nyan cat (which is on Ethereum, I believe), rest on the assumption that one blockchain will be the defacto NFT implementation, and the rest won't be taken seriously?