  The quantum Lefschetz formula explains how virtual fundamental classes (or
structure sheaves) of moduli stacks of stable maps behave when passing from an
ambient target scheme to the zero locus of a section. It is only valid under
special assumptions (genus $0$, regularity of the section and convexity of the
bundle). In this paper, we give a general statement at the geometric level
removing these assumptions, using derived geometry. Through a study of the
structure sheaves of derived zero loci we deduce a categorification of the
formula in the $\infty$-categories of quasi-coherent sheaves. We also prove
that Manolache's virtual pullbacks can be constructed as derived pullbacks, and
use them to recover the classical Quantum Lefschetz formula when its hypotheses
are satisfied.
