Getting a market supply curve from firm supply curve PFA the image below. 



As there are n firms in the market, and a tax of t moves up the cost curves of an individual firm by t units, shouldn't the cost curve of the market move up by n*t units? If yes, why does the book move the curves up only by t units. If no, could you please explain where my reasoning is going wrong?

Thanks
The important thing to note is that the unit on the vertical axis is dollars per unit.

So if there is a tax of $\$t$ per unit, then the market supply curve will move up by $ \$ t$. (And not by $ \$nt $ as you have suggested.)