We use the derived moduli of sections \(\mathbb {R}\mathrm {\underline{Sec}}_{\mathfrak {M}}(\mathfrak {Z}/\mathfrak {C})\) to give derived enhancements of various moduli spaces, including stable maps and stable quasi-maps, which are compatible with their usual perfect obstruction theories. As an application, we prove that G-theoretic stable map and quasi-map invariants of projective spaces are equal.
