Not signed in (Sign In)

Not signed in

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

  • Sign in using OpenID

Site Tag Cloud

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 k-theory lie-theory limit 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 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 subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 17th 2009

    added to global model structure on functors that theorem that the projective and the injective global model structure on functors with values in a combinatorial model category is itself again a combinatorial model category.

    • CommentRowNumber2.
    • CommentAuthorTim_Porter
    • CommentTimeSep 20th 2013

    On the page global model structure on simplicial presheaves, there is mention:

    The paper does not seem to be listed on the Hopf archive, and is not in the pdf of Alex’s papers. Can someone shed some light on this? Heller did have a AMS monograph entitled Homotopy Theorie.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 20th 2013
    • (edited Sep 20th 2013)

    Possibly a typo, I forget what happened. But the entry says it wants to be pointing to that article that

    The fact that the global injective model structure yields a proper simplicial cofibrantly generated model category is originally due to

    so one can just check. Whatever references by Heller you have on model structures on simplicial presheaves, use them to replace the broken citation.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeSep 20th 2013

    I suspect the reference is to Heller’s monograph Homotopy theories, which IIRC did use an injective model structure on simplicial presheaves.

    • CommentRowNumber5.
    • CommentAuthorZhen Lin
    • CommentTimeSep 20th 2013
    • (edited Sep 20th 2013)

    I haven’t checked Heller’s book, but Dugger says the same thing in [Universal homotopy theories]:

    … there is also a Heller model structure [He] in which the cofibrations and weak equivalences are detected objectwise.

    The reference [He] is [Homotopy theories], of course.

    • CommentRowNumber6.
    • CommentAuthorTim_Porter
    • CommentTimeSep 20th 2013

    I have changed the reference, and as the Hopf archive link seems irrelevant (and useless as it stands) I have deleted that, as well. I do have a copy of Heller’s monograph that I will check with just in case.