Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

A bit of light googling turns up several sources asserting that the model structure on simplicial commutative algebras over a ring is left proper (for example, 2.9 in Charles Rezk's paper Every homotopy theory of simplicial algebras admits a proper model). Does a proof of this fact occur anywhere in the literature?

share|improve this question
I don't know where it "appears", though of course it is not hard to prove; it amounts to the fact that polynomial algebras are flat. –  Charles Rezk Sep 27 '12 at 2:48

1 Answer 1

up vote 3 down vote accepted

For simplicial commutative rings this is proved in Lemma 3.1.2 of Schwede's “Spectra in model categories and applications to the algebraic cotangent complex”, and the proof there immediately extends to algebras.

share|improve this answer
Charles was, I suppose, too modest to mention that it is also a special case of the paper I referred to in the question, but this is an earlier reference. –  Rune Haugseng Jun 30 at 10:29

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.