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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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).

nLab > Latest Changes: transitive action

Bottom of Page

1 to 3 of 3

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2021

    added the definition in terms of the shear map being an epimorphism. Adjusted the discussion of requiring or not the underlying object to be inhabited.

    diff, v16, current

    • CommentRowNumber2.
    • CommentAuthoranon-a-moose
    • CommentTimeMay 12th 2024
    I'm confused why the shear map being an epimorphism is sufficient when looking at a transitive group action internal to a category. In some categories (such as Diff), epimorphisms are not necessarily surjections, but the transitivity definition would seem to imply that surjectivity is required.
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 12th 2024
    • (edited May 12th 2024)

    added the parenthetical remark that in more general ambient categories one may want to require stronger notions of epimorphisms (all of which will coincide in the base context of Sets that is considered in the previous paragraph).

    diff, v17, current

1 to 3 of 3

  1.