Not signed in (Sign In)

Start a new discussion

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 bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics 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 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 homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory kan 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 natural nforum nlab nonassociative 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 string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topological topology topos topos-theory 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).
  1. added the Hurewicz model structure as an example of 2-trivial model structure

    Daniel Teixeira

    diff, v2, current

    • CommentRowNumber2.
    • CommentAuthorRichard Williamson
    • CommentTime5 days ago
    • (edited 5 days ago)

    Do you have a reference for or explanation of that? There are a few points which are not obvious to me:

    a) I have never heard of a dual to the Hurewicz/Strøm model structure.

    b) It is not obvious to me that there is any 2-monad around, how is it defined exactly?

    c) Some non-trivial argument must be needed to show that the iso-fibrations are Hurewicz fibrations in the usual sense.

    That the Hurewicz model structure fits into the same circle of ideas is clear (in particular, one can view Hurewicz fibrations as algebras for an endofunctor defined using Moore paths, as in Barthel and Riehl’s work), but my impression has always been that there is a fundamental lack of duality in the details of the construction of the Strøm model structure, which prevents it from fitting exactly into these kind of frameworks. E.g. most of my thesis applies to the Strøm model structure, but not everything, because I have found no way to cook up the necessary strictness in a suitably dualisable way: Moore paths do not dualise very well (there is no obvious way to define a ’Moore cylinder’, although for finite/Alexandroff topological spaces one can maybe do something).

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)