Unless you see the code (e.g. <C-Left>) you're using in the section "Terminal keys" of :set termcap, you can't use it right away.
The docs lists 3 ways to map a special key. First in Insert or Cmdline mode press Ctrl-K, then the key sequence you want to map (e.g. Ctrl-K Ctrl-Left). If it prints <...>, you can use that for the left-hand side of your mapping. Or else, prepend it with <Esc> (Ctrl-V Esc), or use Ctrl-V Ctrl-Left. For example, under tmux I get [1;5D for Ctrl-Left, and <Left> for Left. Which means that for Left I can use <Left>, and for Ctrl-Left I need ^[[1;5D (^[ should be one character, Ctrl-V Esc, and do note the trailing <CR>):
nnoremap ^[[1;5D <Cmd>tabprevious<CR>
Or (:h :set-termcap):
set <C-Left>=^[[1;5D
nnoremap <C-Left> <Cmd>tabprevious<CR>
If you work under different terminals you probably want the second approach:
if &term =~ '^screen'
set <C-Left>=...
elseif &term =~ '^tmux'
set <C-Left>=...
endif
nnoremap <C-Left> <Cmd>tabprevious<CR>
Some keys work with some terminals, but doesn't work with others (when they have no field in the corresponding terminfo entry). Let's take <S-Left>, for example. From :set termcap not under tmux (TERM=rxvt-unicode-256color) I can see that it resides in the t_#4 termcap field:
t_#4 <S-Left> ^[[d
man terminfo says:
key_sleft kLFT #4 shifted left-arrow
key
Which means that the terminfo name is kLFT. Now let's see the value of this field for TERM=rxvt-unicode-256color (not under tmux), TERM=screen (under tmux) and TERM=tmux (which we might need later):
$ infocmp rxvt-unicode-256color | grep kLFT
kLFT=\E[d, kNXT=\E[6$, kPRV=\E[5$, kRIT=\E[c, ka1=\EOw,
$ infocmp screen | grep kLFT
$ infocmp tmux | grep kLFT
kHOM=\E[1;2H, kIC=\E[2;2~, kLFT=\E[1;2D, kNXT=\E[6;2~,
It's missing in the screen terminfo entry. To resolve this:
if &term =~ '^screen'
set <S-Left>=...
endif
nnoremap <S-Left> <Cmd>tabprevious<CR>
Or (with vim we must use termcap names):
if &term =~ '^screen'
set t_#4=...
endif
nnoremap <S-Left> <Cmd>tabprevious<CR>
Alternatively, you can tell tmux to use its own terminfo entry:
set -g default-terminal tmux
On a side note, avoid using the <Esc> character if possible in your config (or generally in a text file). It's one character that looks like 2. If you e.g. copy it with a mouse, ^[ becomes 2 characters and this way it doesn't work. Particularly in the documentation you can find examples where ^[ is 2 characters, that you can't just copy. This sort of thing is easy to overlook.
And by the way, xterm-keys is not available since 2.4.
If it still doesn't work, tell me what you press and the escape sequence it produces (use Ctrl-V).
