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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology 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.
   • CommentAuthorUrs
   • CommentTimeDec 9th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexedited [[model structure on sSet-presheaves]] a little

   edited model structure on sSet-presheaves a little

2. • CommentRowNumber2.
   • CommentAuthorHarry Gindi
   • CommentTimeDec 9th 2010
   • (edited Dec 9th 2010)
   • PermaLink
   Author: Harry Gindi
   Format: MarkdownItexHey Urs, do you know why they (Toen-Vezzosi) specifically used that model structure? It seems like it's a pretty annoying one to describe, and some other pages here show that it's Quillen equivalent to a bunch of much simpler ones.

   Hey Urs, do you know why they (Toen-Vezzosi) specifically used that model structure? It seems like it’s a pretty annoying one to describe, and some other pages here show that it’s Quillen equivalent to a bunch of much simpler ones.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 9th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexHi Harry, i am not sure what you mean, could you expand? This is just the standard projective model structure on simplicial presheaves, set up in the enriched context.

   Hi Harry,

   i am not sure what you mean, could you expand? This is just the standard projective model structure on simplicial presheaves, set up in the enriched context.

4. • CommentRowNumber4.
   • CommentAuthorHarry Gindi
   • CommentTimeDec 9th 2010
   • PermaLink
   Author: Harry Gindi
   Format: MarkdownItexYes, but there are like 30 model structures on simplicial presheaves. This one (the local projective one) seems awfully complicated.

   Yes, but there are like 30 model structures on simplicial presheaves. This one (the local projective one) seems awfully complicated.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeDec 9th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexI am still not sure what you mean. The porjective and injective model structures on simplicial presheaves are those that are easy to state. The intermediate model structures are more complicated. But they are almost never used (Jardine in his lectures points out a single article that uses an intermediate model structure).

   I am still not sure what you mean. The porjective and injective model structures on simplicial presheaves are those that are easy to state. The intermediate model structures are more complicated. But they are almost never used (Jardine in his lectures points out a single article that uses an intermediate model structure).

6. • CommentRowNumber6.
   • CommentAuthorHarry Gindi
   • CommentTimeDec 10th 2010
   • PermaLink
   Author: Harry Gindi
   Format: MarkdownItex@Urs: There is a global model on simplicial presheaves defined by objectwise fibrations and weak equivalences. This is the "global projective model structure". All of Toen's work (including his lecture notes on DAG and simplicial commutative rings, etc) use the local projective model structure (the one that also encodes descent and hypercovers and stuff).

   @Urs: There is a global model on simplicial presheaves defined by objectwise fibrations and weak equivalences. This is the “global projective model structure”. All of Toen’s work (including his lecture notes on DAG and simplicial commutative rings, etc) use the local projective model structure (the one that also encodes descent and hypercovers and stuff).