Joining in questioning… kitty dev seems to hate tmux since kitty can perform many of it's behaviors. The thing that's most interesting to me is tmux for detaching and persisting a session on a remote host. Does kitty cover this functionality too? Is there like kittyd?
If persisting sessions is the only thing you use tmux or screen for (as it was for me), try `dtach`. Session management is all it does; terminal I/O is passed through just like a plain ssh session.
