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 history homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie lie-theory limit 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 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.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 22nd 2010

    I see shape theory being brought up at the Cafe. So did people ever think of a coshape theory? Yes, I see from a talk

    The notion of coshape of a space was introduced by T. Porter.

    Still, it doesn’t seem to be nearly so well studied. Is it less interesting for some reason?

    • CommentRowNumber2.
    • CommentAuthorTim_Porter
    • CommentTimeOct 22nd 2010

    In many ways classical coshape is the same as singular homotopy theory. The original form of shape with Borsuk etc. looked at the properties of a space in terms of mapping it into polyhedra (up to homotopy). It was Cech homotopy. The coshape then would be mapping polyhedra into the space (up to homotopy) so was related (sort of universally) to mapping the singular complex in. There are categorical coshape situations that do give useful results but I do not now what the strong coshape theory would be nor how it might adapt to the topos situation. I did write one paper whch looked at both at the same time. I do not think coshape is less interesting in general but classically it was (sort of ) known.

    As no doubt you found there is a paper Yu T Lisitsa 1980 Russ. Math. Surv. 35 250

    on Strong Coshape Theory.