Can we do a preinverse to diagonal?

[benediktahrens]

i.e. a morphism of relative comonads
e : E |- Stream -> Tri
mapping (a1, a2,...) to
a1 e e ...
a2 e ....
a3
It looks like this ain't a morphism of coalgebras in the category TRI, so cannot be defined via terminality of Tri. But a "manual" definition might be possible...