How does the receiver of a transaction check the whole chain of ownership? While reading Satoshi Nakamoto's paper on how bitcoin works, I got stuck on #2. In a chain of transactions, how can someone who has received the coin check the whole chain with just a signed hash of the previous one? 

Either


The person sending the coin would have to include the whole ownership chain, which would start increasing more and more in size
There would have to be a public hash-to-transaction mapping somewhere.
There would have to be a list of valid coins somewhere, making checking only the most recent transaction necessary


I don't see Satoshi Nakamoto talking about any of these.
There would have to be a public hash-to-transaction mapping somewhere.


Yes. There is a database of utxo - unspent transaction outputs. To be correct - it is an index of blockchain file.