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 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 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.
    • CommentAuthorUrs
    • CommentTimeMay 12th 2012
    • (edited May 12th 2012)

    Added some content to display map from Taylor’s book. Not very deep, mostly as a reference to the respective section for me.

    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeMay 13th 2012

    Nice! You left out an important part in one clause of the definition, which actually makes the other clause redundant (although I know that Taylor stated it). Explicitly, a pullback of a display must not only exist but also be a display.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 14th 2012

    Thanks for fixing that. I certainly meant to say that. Not sure why I didn’t.

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 14th 2012
    • (edited May 14th 2012)

    I put in the example of a category with a singleton pretopology - which is a concept identical to a class of display maps which are closed under composition (including nullary)

    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeMay 16th 2012

    Thanks, David, I don’t know why I never made that connection!

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 16th 2012

    Toby - it’s quite amazing how many classes of maps are pretopologies and people don’t state the fact e.g. Remarks 4.2 and 4.3 (stable under pullbacks and closed under composition resp.) in the stacks project chapter http://www.math.columbia.edu/algebraic_geometry/stacks-git/spaces.pdf - over 20 pretopologies on SchSch listed.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeAug 24th 2023

    added the original reference:

    • Paul Taylor, §4.3.2 in: Recursive Domains, Indexed Category Theory and Polymorphism, Cambridge (1983-7) [pdf]

    diff, v15, current

    • CommentRowNumber8.
    • CommentAuthormattecapu
    • CommentTimeSep 12th 2024

    redirects ’category with display map(s)’

    diff, v17, current