I have set up my tmux to use screen-256colors and it works great with vim.
However, when I ssh to a remote host from within tmux, screen-256colors isn't recognized, so I'm getting errors like this:
E558: Terminal entry not found in terminfo 'screen-256color' not known. Available builtin terminals are:
builtin_ansi
builtin_xterm
builtin_iris-ansi
builtin_dumb defaulting to 'ansi'
Other than editing each remote .bashrc (similarly to this suggestion), is there any way to set the TERM correctly and automatically on the remote host?