I’m reading “Sheaves in geometry and logic”, in page 80:

  Please refer to [1]: https://i.sstatic.net/INrU0.jpg

It says “…,therefore $FU=\coprod_{x\in U} fx$. The space…”.

So could anyone please explain why therefore $FU$ is a coproduct?

It seems that $FU$ should be just the product of $F(\{x\})$?