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.
    • CommentAuthorUrs
    • CommentTimeOct 14th 2010

    started stub for bounded geometric morphism

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 9th 2016

    I corrected the characterisation of boundedness.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeJan 9th 2016

    Why don’t you just say quotient of a subobject of …, instead of subquotient of a subobject of …?

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 9th 2016
    • (edited Jan 9th 2016)

    Oh I see. It was fine as it was. I’ll roll back, but fix a typo.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 10th 2016
    • (edited Jun 10th 2016)

    Jonas Frey has kindly added some material to the Properties-section at bounded geometric morphism. I have touched the formatting a little and added some more cross-links with the entry internal sheaf.

    Notice that the entry is still waiting for somebody to complete two items in its Definition section!

    • CommentRowNumber6.
    • CommentAuthorJonasFrey
    • CommentTimeJun 13th 2016

    I filled in the holes in the definition by copying the missing parts from the elephant, and rephrasing a bit.

    The equivalent reformulations use terminology that needs to be defined, therefore I amended separating family, adding the definition of separating family in a fibration.

    The concept of gluing fibration still needs to be defined – probably by remarking on the page on Artin gluing that the appropriate projection is a fibration. I’ll come back to that maybe tomorrow.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJun 13th 2016


    • CommentRowNumber8.
    • CommentAuthorjonsterling
    • CommentTimeNov 17th 2021

    I think that the statement about the gluing fibration should be 1\partial_1 not 0\partial_0 right? We are restricting the codomain fibration along the inverse image of the geometric morphism, not the domain functor. Right?

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeNov 17th 2021
    • (edited Nov 17th 2021)

    We are talking about this line, supposedly).

    But 0\partial_0 is the codomain, in usual simplicial conventions (remove the 0-vertex!)

    In any case, for the moment I have removed the symbol “ 0\partial_0” (it’s not too illuminating and never appears again, anyway). Somebody should indicate the actual definition of that morphism!

    diff, v12, current