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Nov 7, 2022 at 7:41 comment added David Corwin See also kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/0799-09.pdf, which discusses the degree n generalization of (3)/(4) of the original question in a more concrete way.
Nov 12, 2019 at 9:41 comment added Tim Porter I somehow omitted to mention Illusie's thesis: L. Illusie, 1971, Complexe cotangent et déformations I , volume 239 of Lecture Notes in Maths , Springer-Verlag with a second volume No 283. which provides a lot of the 1970s development work in the simplicial context and relates to a lot of work since then
Nov 9, 2019 at 14:53 history answered Tim Porter CC BY-SA 4.0