Sorry I can't get what you want.

If you just want a key to switch to another tab, then there have been such default key mappings:

map J previousTab
map K nextTab
map gT previousTab
map gt nextTab

However, the Arc browser has its own private logic of sorting tabs, while extensions can not get any real order. As a result, nextTab may jump to one of some unexpected tabs.

Yes, nextTab and previousTab don't work properly in the arc browser......
But the keyboard shortcuts Ctrl + Alt + Up and Ctrl + Alt + Down work fine for navigating to the next and previous tab, which is why I wanted to map them to J and K.
Hope I'm getting my point across.

Vimum C's keyboard layout rules, map and mapKey directives can only take effect inside Vimium C itself.

There's no API to "tell Arc to run Ctrl+Alt+Up".

Oh ok, I see.
Thanks

I got around this by remapping the next/previous tabs to ctrl+j/k in Arc's settings. This is a bit less comfortable than shift-j/k with a standard MacOS keyboard layout, but I've used Karabiner-Elements to remap the backtick (`) key to register as ctrl when held down. Massive QOL improvement for navigating tabs in Arc.