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 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

1. • CommentRowNumber1.
   • CommentAuthorTim_Porter
   • CommentTimeJun 11th 2011
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexThis is a mostly question for Zoran in particular as he is nearest to the Shape considerations where it occurs. Goerss and Jardine discuss towers of simplicial sets and a model category structure on them, but their morphisms are not those of the structure needed for pro-categories (i.e. as per Grossman's paper and more recently Isaksen's model structure on Pro-sSet.) If we are to discuss those latter ones somewhere, (and it would seem natural to do so) then there needs to be some convention on which is which! Any ideas? At present in the Lab, towers refer only to the functor category à là Goerss-Jardine.

   This is a mostly question for Zoran in particular as he is nearest to the Shape considerations where it occurs. Goerss and Jardine discuss towers of simplicial sets and a model category structure on them, but their morphisms are not those of the structure needed for pro-categories (i.e. as per Grossman’s paper and more recently Isaksen’s model structure on Pro-sSet.) If we are to discuss those latter ones somewhere, (and it would seem natural to do so) then there needs to be some convention on which is which! Any ideas? At present in the Lab, towers refer only to the functor category à là Goerss-Jardine.

2. • CommentRowNumber2.
   • CommentAuthorjim_stasheff
   • CommentTimeJun 11th 2011
   • PermaLink
   Author: jim_stasheff
   Format: TextNot to mention Postnikov towers and Whitehead towers and...

   Not to mention Postnikov towers and Whitehead towers and...
3. • CommentRowNumber3.
   • CommentAuthorTim_Porter
   • CommentTimeJun 11th 2011
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexYep. The sneaky Grossman structure is obtained from the one use by Goerss and Jardine by localising with respect to the natural maps from a space to its Postnikov tower (more or less).

   Yep. The sneaky Grossman structure is obtained from the one use by Goerss and Jardine by localising with respect to the natural maps from a space to its Postnikov tower (more or less).

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeJun 14th 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI see the question only now. Will try to think later, I have no immediate comments. Interesting gadget.

   I see the question only now. Will try to think later, I have no immediate comments. Interesting gadget.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeAug 30th 2016
   • (edited Aug 30th 2016)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added to _[[tower]]_ a section _[The pro-category of towers](https://ncatlab.org/nlab/show/tower#TheProCategoryOfTowers)_. So far it contains just the definition, the statement that all pro-morphisms of towers are represented by towers of morphisms (proof?) and the statement that finite limits and colimits are represented by degreewise such under this presentation.

   I have added to tower a section The pro-category of towers. So far it contains just the definition, the statement that all pro-morphisms of towers are represented by towers of morphisms (proof?) and the statement that finite limits and colimits are represented by degreewise such under this presentation.