Mount a remote filesystem using SFTP

Here's the scenario (a very common one, I think):

I have some code I am testing on a unix system at work, but I am editing it from my Linux PC at home. I cannot run the code on my home PC. I have several options, none of which is entirely satisfactory:

1. Open a remote emacs window running on the unix system at work (painfully slow), and save the code straight into the directory where I will compile it.

2. Edit the code remotely using a text-only editor. Much faster, but no mouse control or syntax highlighting.

3. Run emacs at home, and copy the code back and forth with sftp (very messy, and easy to copy the wrong way by mistake, overwriting the work I've just done)

But there should be a better way. Why can't my local emacs session read-write DIRECTLY over the internet to the unix system at work? All I need is a transparent "sftp filesystem" mounted on my linux PC, such that every read-write operation in the directory is translated into an sftp command.

Anyone know of a program to do this? It should be quite straightforward to implement, using something like "fuse".

Matthew.