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 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 nforum 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 sheaves 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.
    • CommentAuthorelif
    • CommentTimeAug 29th 2013
    In profinite algebraic homotopy page 111 Pro-C completions of a crossed modules and pro-C completions of the individual pieces of data involved are not always same. Can you give me a basic example about this?
    • CommentRowNumber2.
    • CommentAuthorTim_Porter
    • CommentTimeAug 29th 2013

    A good question. I thought the example on p.281 (in that version) might help, but I’m not sure it does. That section then goes on to look at Friedlander’s fibration example and that may also be helpful. Have a look at the Sl(2,5) example in more detail.

    • CommentRowNumber3.
    • CommentAuthorelif
    • CommentTimeAug 29th 2013
    I mentioned about profinite algebraic homotopy (shortened version). It has 239 pages. Are there any other version? İf you send me a link about it ,I will look at these example. On the other hand I want to ask you one more question? We can define other completion on algebras with its any ideal. (In commutative algebra this is called I-adic completion) So , can we apply this property on crossed modules of algebras ? And if it is defined, how can I apply same question in Pro-C completion? (page 111)
    Thanks for your concern...
    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeAug 30th 2013

    elif: There are longer versions, but in any case the examples are in section 5.5 of the version that you have.

    My advice to you is not to ask us the question, but to take apart what II-adic completion does in the commutative algebra case, and, importantly, what is it used for. Once you understand that well, you can try to see if an II-adic completion for crossed modules of commutative algebras/ cat^1-algebras is going to do something interesting. Again you need to find some examples of these things, say in polynomial rings and to produce some calculations (for yourself).

    When the work on pro-C completions of crossed modules was done, all the links between that stuff and higher dimensional algebra were less clear than they are now, so you need to look at that old stuff from the perspective of todays viewpoint, so as to make sure you are approaching it in a sufficiently general categorical way.