I will prove that derived $C^\infty$-geometry, defined by gluing simplicial $C^\infty$-spaces up to homotopy, can be faithfully expressed through the usual category of simplicial $C^\infty$-rings. In particular, I will show equivalence to D.Spivak's construction. (Joint work with J.Noel)
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/3639