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 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 nforum 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 sheaves simplicial space spin-geometry stable-homotopy-theory stack 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.
    • CommentAuthorFinnLawler
    • CommentTimeAug 7th 2010

    I’ve started cleaning up and adding stuff at fibration in a 2-category, but it’s bedtime now, so I’ll finish it tomorrow.

    • CommentRowNumber2.
    • CommentAuthorFinnLawler
    • CommentTimeAug 9th 2010

    Okay, ’I’ll finish it tomorrow’ was a bit ambitious, but I’m now finished with fibration in a 2-category for the moment.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeNov 3rd 2010

    There’s a bit of ambiguity at fibration in a 2-category – are we talking about strict Grothendieck fibrations or weak Street fibrations? I believe all the same facts are true in either case, as long as we make the correct choices about what to interpret strictly or weakly in each case. Since “2-category” means “weak 2-category” by default on the nLab, in which case the Street version is the only sensible one, it might make sense to focus on that version – although we would then have to clarify that fibrations in the 2-category Cat are not actually Grothendieck fibrations but Street ones.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeNov 3rd 2010

    I tried to clarify the difference a bit in the “Idea” and “Definition” sections, but I still need to look at the “Details” section.

    • CommentRowNumber5.
    • CommentAuthorFinnLawler
    • CommentTimeNov 3rd 2010

    That’s a good point, which I didn’t think about when I added the stuff from Fibrations in bicategories. It’s definitely worth clarifying. I like what you’ve added so far.

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeNov 4th 2010

    I modified the first lemma on the page to work with Street fibrations and non-strict slice 2-categories, but now I have to go. However, I’m not actually sure where that lemma should go – it’s not really about fibrations in a 2-category, but is just an alternate characterization of ordinary fibrations in Cat. So maybe it should go at Grothendieck fibration and/or Street fibration (in the two versions) – or maybe at cleavage? (By the way, I edited cleavage some too, and in particular I added the version for Street fibrations.)

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeNov 7th 2010

    I put the strict version of the lemma at Grothendieck fibration and the non-strict version at Street fibration.

    • CommentRowNumber8.
    • CommentAuthormattecapu
    • CommentTimeJan 20th 2023

    Added precisation about the 2-dimensional structure of the augmented simplex 2-category

    diff, v23, current

    • CommentRowNumber9.
    • CommentAuthorvarkor
    • CommentTimeAug 27th 2023

    Added an early reference.

    diff, v25, current

    • CommentRowNumber10.
    • CommentAuthorvarkor
    • CommentTimeDec 2nd 2023

    Added an earlier reference of Street.

    diff, v27, current