Grothendieck topology is a categorical analogue of usual topology. It originated in algebraic geometry and was already used in the o-minimal context. Also microlocal analysts have already worked with "the subanalytic site". Grothendieck topology allows to define a deeper version of the notion of a topological space. Here several things should be clarified. Then we get an o-minimal version of homotopy theory. As an example, I want to show a Bertini-Lefschetz type theorem about fundamental groups.