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-type-theory cohomology colimits combinatorics 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 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 kan 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 newpage nlab nonassociative noncommutative noncommutative-geometry number-theory object 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 subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory 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).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 8th 2009
    • (edited May 13th 2010)

    I removed my recent material at simplex in a lined topos and instead inserted this now, expanded, at

    interval object

    where it belongs. There is now a section there that discusses how interval objects gives rise to cubical and simplicial path oo-categories.

    The proposition I state there I have carefully checked. Should be correct. But haven't typed the proof, it doesn't lend itself to being typed (straightforward but tedious, as one says).

    But if it is indeed correct, this must be standard well-known stuff. Does anyone have a reference?!

    I also restructured and edited the rest of the entry a bit, trying to make it a bit nicer. THis entry deserves more attention, it is a pivotal entry.

    Tomorrw when I am more awake I'll remove simplex in a lined topos and redirect links to it suitably to interval oject.

    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeOct 8th 2009

    Last link: interval object

    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeOct 8th 2009

    Added remark to interval object that the affine line A^1 is an interval object in the A^1 homotopy theory of schemes, but is obviously not like the interval in the topological sense.

    • CommentRowNumber4.
    • CommentAuthorGuest
    • CommentTimeOct 8th 2009
    Whoops, apologies, that last comment was me.

    -David Roberts

    (tardy in signing up to the forum, I know)
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeOct 8th 2009

    Thanks David.

    I had known about this from Zoran, but never looked into it in any detail.

    But I have now at least picked up this thread and created stubs for

    homotopy localization

    and

    A1 homotopy theory

    and linked to them from the paragraph that you added to interval object.

    I also restructzred interval object a but further to amplify this point.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 8th 2009

    I also worked further on interval object:

    expanded the introduction further, renames some headlines, added formal definition/theorem/proof environments, expanded the remarks on the meaning of the construction of that cosimplicial object.

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)