  Eventually after Dieudonn\'e-Grothendieck, we give intrinsic definitions of
\'etale, lisse and non-ramifi\'e morphisms for general adic rings and general
locally convex rings. And we investigate the corresponding \'etale-like,
lisse-like and non-ramifi\'e-like morphisms for general $\infty$-Banach,
$\infty$-Born\'e and $\infty$-ind-Fr\'echet $\infty$-rings and
$\infty$-functors into $\infty$-groupoid (as in the work of
Bambozzi-Ben-Bassat-Kremnizer) in some intrinsic way by using the corresponding
infinitesimal stacks and crystalline stacks. The two directions of
generalization will intersect at Huber's book in the strongly noetherian
situation.
