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 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 constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory infinity integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories newpage noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar 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-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.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 28th 2017

    The entry cofibration is need of some attention. It wasn’t even linked to from codiscrete cofibration, so I’ve remedied that. There’s also Hurewicz cofibration to bring into the fold.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 28th 2017

    so then best to add a section with Examples

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 28th 2017

    Would it be OK just to dualise the opening to fibration?

    In classical homotopy theory, a fibration p:EBp:E\to B is a continuous function between topological spaces that has a certain lifting property. The most basic property is that given a point eEe\in E and a path [0,1]B[0,1] \to B in BB starting at p(e)p(e), the path can be lifted to a path in EE starting at ee.

    So

    In classical homotopy theory, a cofibration i:ABi:A\to B is a continuous function between topological spaces that has a certain extension property.

    Then?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 28th 2017

    If the concept of fibration is specified, then the cofibrations are the maps that have the left lifting property again those fibrations that are also weak equivalences. And conversely, if the cofibrations are pre-specified, then the fibrations are those that have the right lifting property against the cofibrations that are also weak equivalences.

    A classical example of cofibrations in topology are the Hurewicz cofibrations which are defined by a certain homotopy extension property.

    • CommentRowNumber5.
    • CommentAuthorTim_Porter
    • CommentTimeMay 28th 2017

    Classically cofibrations were defined in various ways and the idea was independent (and pre-dated) any ideas from model category speak. Of course, once one has that class of maps one can get a useful class of ‘fibrations’, but the concept does not require that and for instance in any setting having a well behaved cylinder one has a well behaved notion of cofibration, but fibrations are not as easy to describe.

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)