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.
    • CommentAuthorTim_Porter
    • CommentTimeOct 10th 2012

    Confusion ! (in my head so help please). Quote from torsor:

    “A left G-torsor over a group G is an inhabited object P equipped with a G-action, ρ:G×P→P etc. “

    Am I dreaming or is there a problem with the wording? Note at group extension we find:

    “For AiG^pGA \stackrel{i}{\to} \hat G \stackrel{p}{\to} G a group extension, we have that p:G^Gp : \hat G \to G is an AA-torsor over GG ….”

    If I understand correctly, the word ’over’ is being used in different ways. Perhaps in the first instance the ’over a group GG’ is redundant. The torsor is in a general category at this point. In the second case the ‘over GG’ refers to the fact that we are working in a slice category. Then the group involved is not AA but A×GGA\times G\to G. Once I have clarified this I will alter the wording if necessary, but at the moment i find the uses less than clear.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 10th 2012

    The very first sentence had

    A GG-torsor for GG a group…

    I have changed both sentences now to

    For GG a group, a GG-torsor is…

    • CommentRowNumber3.
    • CommentAuthorTim_Porter
    • CommentTimeOct 10th 2012

    Thanks. The revised wording looks good.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeOct 12th 2012
    • (edited Oct 12th 2012)

    I think it would be better something of the kind

    “A torsor with structure group GG, or in short GG-torsor, is…”__

    This may or may not (it is a bit redundant) be preceded by “Given a group GG,”.