generally in differential cohesion
the canonical diagram
for each point there exists an open subset such that
The category SmoothMfd of smooth manifolds may naturally be thought of as sitting inside the more general context of the cohesive (∞,1)-topos Smooth∞Grpd of smooth ∞-groupoids. This is canonically equipped with a notion of differential cohesion exhibited by its inclusion into SynthDiff∞Grpd. This implies that there is an intrinsic notion of formally étale morphisms of smooth -groupoids in general and of smooth manifolds in particular
See this section for more details.