The quantum Lefschetz principle allows one to know the Gromov-Witten
invariants of the zero locus of a section of a vector bundle from those
of the ambient space. More generally, it expresses a relation between
the virtual fundamental classes of the moduli stacks of stable maps to
these schemes, algebraic cycles obtained from a construction which can
appear somewhat mysterious. In this talk, I will explain how, through
derived geometry, one can interpret this result as a purely geometric
phenomenon, and deduce a categorification of the formula for virtual
classes.