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 bundle bundles calculus 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 finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity 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 infinity integration integration-theory itex k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory 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 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 string string-theory 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.
    • CommentAuthorspitters
    • CommentTimeFeb 4th 2017

    equifibered natural transformation misses references. I’ve traced cartesian natural transformation back to: Street - the petit topos of globular sets which refers to: Carboni, Johnstone - Connected limits, familial representability and Artin glueing unfortunately, I do not have access to the latter.

    Is this the best source?

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeFeb 4th 2017

    It’s a good source, yes. My memory is that Tom Leinster’s book on higher categories also treats cartesian transformations, and it’s easily available.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 4th 2017

    Hopefully one of you finds a minute to add the reference to the entry!

    • CommentRowNumber4.
    • CommentAuthorCharles Rezk
    • CommentTimeFeb 4th 2017
    • (edited Feb 4th 2017)

    I’ve used the phrase “equifibered map” (where the map is itself a natural transformation) in various places, with this meaning (but in an \infty-context). For instance, in my old model topos notes http://www.math.uiuc.edu/~rezk/homotopy-topos-sketch.pdf, or here: http://www.math.uiuc.edu/~rezk/i-hate-the-pi-star-kan-condition.pdf.

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeFeb 5th 2017

    References now added.

    • CommentRowNumber6.
    • CommentAuthorspitters
    • CommentTimeFeb 5th 2017

    Thanks! To be sure, is this notion indeed different from the notion of cartesian natural transformation in the theory of fibred categories. E.g. Streicher.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeFeb 5th 2017

    Thanks, Todd!

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeFeb 5th 2017
    • (edited Feb 5th 2017)

    I have also added pointer to Rezk 10 and Rezk 14.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJun 30th 2020
    • (edited Jun 30th 2020)

    I have added the statement (here) of descent in \infty-toposes characterized via equifibered transformations of colimiting diagrams

    But I am going to give this sub-section its stand-alone entry now, and then re-!include it, because the same discussion ought to be included in various other relevant entries

    diff, v5, current

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)