You might look at Costello-Gwilliam book (especially 'Derived Euler-Lagrange equations' and 'Derived critical locus' - in the Appendix)

http://math.northwestern.edu/~costello/factorization_public.html

You might look at Costello-Gwilliam book (especially 'Derived Euler-Lagrange equations' and 'Derived critical locus' - in the Appendix)

http://math.northwestern.edu/~costello/factorization_public.html (Wayback Machine)