within tmux.
There is a global environment, copied from the external environment when the
server is started and each sesssion has an (initially empty) session
environment which overrides it.
New commands set-environment and show-environment manipulate or display the
environments.
A new session option, update-environment, is a space-separated list of
variables which are updated from the external environment into the session
environment every time a new session is created - the default is DISPLAY.
Nicholas Marriott