  In General Relativity a space-time $M$ is regarded singular if there is an
obstacle that prevents an incomplete curve in $M$ to be continued. Usually,
such a space-time is completed to form $\bar{M} = M \cup \partial M$ where
$\partial M$ is a singular boundary of $M$. The standard geometric tools on $M$
do not allow "to cross the boundary". However, the so-called Synthetic
Differential Geometry (SDG), a categorical version of standard differential
geometry based on intuitionistic logic, has at its disposal tools permitting
doing so. Owing to the existence of infinitesimals one is able to penetrate
"germs of manifolds" that are not visible from the standard perspective. We
present a simple model showing what happens "beyond the boundary" and when the
singularity is finally attained. The model is purely mathematical and is
mathematically rigorous but it does not pretend to refer to the physical
universe.
