Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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

1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeApr 5th 2014
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThis is motivated by my speculations in [another thread](http://nforum.mathforge.org/discussion/5817/cojet-differential-forms/), but it's a standalone concrete question for the people who've thought more about convenient categories of smooth spaces than I have. In which such categories is there a "tangent bundle" functor which (extends the usual tangent bundle functor on manifolds and) preserves sequential limits? This should be the case in models of SDG where the tangent bundle $T X = X^D$ is a right adjoint; but is it true in any "concrete" category of smooth spaces?

   This is motivated by my speculations in another thread, but it’s a standalone concrete question for the people who’ve thought more about convenient categories of smooth spaces than I have. In which such categories is there a “tangent bundle” functor which (extends the usual tangent bundle functor on manifolds and) preserves sequential limits? This should be the case in models of SDG where the tangent bundle $T X = X^D$ is a right adjoint; but is it true in any “concrete” category of smooth spaces?

2. • CommentRowNumber2.
   • CommentAuthorAndrew Stacey
   • CommentTimeApr 5th 2014
   • PermaLink
   Author: Andrew Stacey
   Format: MarkdownItexYou may be interested in [[tangential notions of Frölicher spaces]].

   You may be interested in tangential notions of Frölicher spaces.

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeApr 5th 2014
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThanks! I had a look at it, but it doesn't say anything about limits. If I had enough time, I could probably sit down with the definition of Frolicher space, construct limits therein, and check whether any kind of tangent space preserves them, but I was hoping that someone (like you) would already know the answer.

   Thanks! I had a look at it, but it doesn’t say anything about limits. If I had enough time, I could probably sit down with the definition of Frolicher space, construct limits therein, and check whether any kind of tangent space preserves them, but I was hoping that someone (like you) would already know the answer.