Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorMatanP
   • CommentTimeJul 17th 2012
   • PermaLink
   Author: MatanP
   Format: MarkdownItexI looked at the stab on monoidal [[monoidal Dold-Kan correspondence]] and was wondering if one could get a Quillen equivalence via a DK-correspondence (or alike) from Cdga/k = the category of (cochain) commutative dg algebras concentrated in non-positive degrees over a ring k of characteristic zero to the category simplicial commutative k-algebras. The stab only talks about char 0 field and doesn't mention an equivalence in this case (but rather a correspondence) and on the other hand it seems that Toen's DAG uses this implicitly.

   I looked at the stab on monoidal monoidal Dold-Kan correspondence and was wondering if one could get a Quillen equivalence via a DK-correspondence (or alike) from Cdga/k = the category of (cochain) commutative dg algebras concentrated in non-positive degrees over a ring k of characteristic zero to the category simplicial commutative k-algebras.

   The stab only talks about char 0 field and doesn’t mention an equivalence in this case (but rather a correspondence) and on the other hand it seems that Toen’s DAG uses this implicitly.

2. • CommentRowNumber2.
   • CommentAuthorMatanP
   • CommentTimeJul 18th 2012
   • PermaLink
   Author: MatanP
   Format: MarkdownItexSorry for the confusion. I now see that the only gap between the nLab entry and the equivalence used in Toen and Vezzosi's DAG is that they only assume k is a ring of char 0. It seems that the Quillen equivalence in the case of char 0 field (in "Rational homotopy theory") extends for the more general case but I want to be sure. We can then add it to the nLab entry and make the connection with DAG.

   Sorry for the confusion. I now see that the only gap between the nLab entry and the equivalence used in Toen and Vezzosi’s DAG is that they only assume k is a ring of char 0. It seems that the Quillen equivalence in the case of char 0 field (in “Rational homotopy theory”) extends for the more general case but I want to be sure. We can then add it to the nLab entry and make the connection with DAG.

3. • CommentRowNumber3.
   • CommentAuthorMatanP
   • CommentTimeJul 19th 2012
   • (edited Jul 19th 2012)
   • PermaLink
   Author: MatanP
   Format: MarkdownItexI now see that the introduction of [BZFN](http://arxiv.org/pdf/0805.0157v5.pdf) says that the Dold-Kan becomes an equivalence between simplicial commutative k-algebras and connected cdga's for k a $\mathbb{Q}$-algebra. Is it ok to add it to [[monoidal Dold-Kan correspondence]] ?

   I now see that the introduction of BZFN says that the Dold-Kan becomes an equivalence between simplicial commutative k-algebras and connected cdga’s for k a $\mathbb{Q}$-algebra. Is it ok to add it to monoidal Dold-Kan correspondence ?

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 21st 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItex> I looked at the stab on monoidal monoidal Dold-Kan correspondence > The stab only talks about char 0 Do you mean "stab" or "stub"? Could you say what you mean by the word?

   I looked at the stab on monoidal monoidal Dold-Kan correspondence

   The stab only talks about char 0

   Do you mean “stab” or “stub”? Could you say what you mean by the word?

5. • CommentRowNumber5.
   • CommentAuthorMatanP
   • CommentTimeJul 22nd 2012
   • PermaLink
   Author: MatanP
   Format: MarkdownItexSorry for the bad English -- I meant stub. As for the math., Toen and Vezzosi (and [BZFN](http://arxiv.org/pdf/0805.0157v5.pdf) ) say that the Quillen equivalence works for k a $\mathbb{Q}$ algebra which I guess is what most people call a ring of charachteristic 0. I'll try to see if Quillen's original argument is valid as is for that case but I wanted to see if someone knows it already.

   Sorry for the bad English – I meant stub. As for the math., Toen and Vezzosi (and BZFN ) say that the Quillen equivalence works for k a $\mathbb{Q}$ algebra which I guess is what most people call a ring of charachteristic 0. I’ll try to see if Quillen’s original argument is valid as is for that case but I wanted to see if someone knows it already.