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).
  1. +–{.query} Todd (posted from n-category cafe): I don’t know if the story is any different for XX compact Hausdorff, but it could be worth considering. =–

    I am interested in this statement - i.e. in a (minimal) assumption on a category of topological spaces such that the notion of compact object in it reduces to that of a compact topological space. Have you already been considering this question?

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeMar 8th 2012

    Stephan, some weeks back I was ruminating on similar things (again), but came to no conclusion, and these matters still lie fallow for me. Maybe I’ll have another go at it.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMar 8th 2012

    In case it matters, I think Stephan might actually be wanting to know about the relation between traditional and category-theoretic compactness not so much in the category of topological spaces, but in just that of (topological / smooth/ ….) manifolds.

  2. Thanks, Todd. For me to get started: Do you know just any (maybe more restrictive then necessary) category of spaces on which the statement holds?