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 comma 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 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 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 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.
    • CommentAuthorUrs
    • CommentTimeJul 12th 2018

    merged some material into this entry. What is actually the original reference? Is it Ehresmann 63 or Bastiani-Ehresmann 74?

    diff, v4, current

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeJul 13th 2018

    Well, 63<7463\lt 74

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 13th 2018
    • (edited Jul 13th 2018)

    All right, so I’ll check myself… No, it’s not in that article from 63 that I pointed to (which I got from your article). The term “quintet” is just announced there, with pointer to another article. But it’s not so important, just thought I’d check while I am at it. The world will survive without knowing where Ehresmann noted down this simple idea first.

    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeJul 13th 2018
    • (edited Jul 13th 2018)

    In Ehresmann’s collected works there is at no 58: Catégorie double des quintettes; applications covariantes, C.R.A.S. Paris 256 (1963), 1891-1894. Andrée Ehressmann comments on this in the Collected Works.

    The paper is in volume III.

    • CommentRowNumber5.
    • CommentAuthorTim_Porter
    • CommentTimeJul 13th 2018

    Added link to an earlier source.

    diff, v6, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 13th 2018

    Thanks! So I adjusted the text around the references accordingly.

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeJul 13th 2018

    Thanks everyone! Maybe I got the “63” reference wrong originally.

    • CommentRowNumber8.
    • CommentAuthorTim_Porter
    • CommentTimeJul 13th 2018

    Mike, you did not. He mentions it in the paper to which you referred, but there he refers to the Comptes Rendus paper for more details.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJul 13th 2018

    for more details.

    For any details. Unless I am missing something.

    • CommentRowNumber10.
    • CommentAuthorTim_Porter
    • CommentTimeJul 13th 2018

    Yes you’re right!

    • CommentRowNumber11.
    • CommentAuthorBryceClarke
    • CommentTimeMar 31st 2023

    Noted that the quintet construction admits a left adjoint (in addition to admitting a right adjoint) and provided the reference.

    diff, v9, current