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.
   • CommentAuthorUrs
   • CommentTimeApr 30th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexat _[[Postnikov tower]]_ in the section _[Construction for simplicial sets](http://ncatlab.org/nlab/show/Postnikov+system#ConStructionForSimplicialSets)_ I made explicit three different models. Two of them were discussed there before, the third I have now added. Briefly. Deserves to be expanded.

   at Postnikov tower in the section Construction for simplicial sets I made explicit three different models. Two of them were discussed there before, the third I have now added. Briefly. Deserves to be expanded.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 28th 2012
   • (edited Nov 28th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI had gotten myself mixed up about some fibration issue the other day, so I will speak out loud the following here before adding it to the entry: consider $f \colon X \to Y$ a morphism of _strict_ $\infty$/$\omega$-groupoids (globular sets equipped with etc.). Then for $n \in \mathbb{N}$ the [[n-image]]/$(n-1)$-relative Postnikov stage of $f$ is presented by the strict $\infty$-groupoid $im_n(f)$ such that * the $(k \lt n-1)$-morphisms are those of $X$; * the $(k = n-1)$-morphisms are equivalence classes of those of $X$, with two regarded as equivalent if their images under $f$ coincide; * the $(k \geq n)$-morphisms are those of $Y$. I hope I got this right now...

   I had gotten myself mixed up about some fibration issue the other day, so I will speak out loud the following here before adding it to the entry:

   consider $f \colon X \to Y$ a morphism of strict $\infty$/$\omega$-groupoids (globular sets equipped with etc.).

   Then for $n \in \mathbb{N}$ the n-image/$(n-1)$-relative Postnikov stage of $f$ is presented by the strict $\infty$-groupoid $im_n(f)$ such that

   • the $(k \lt n-1)$-morphisms are those of $X$;

   • the $(k = n-1)$-morphisms are equivalence classes of those of $X$, with two regarded as equivalent if their images under $f$ coincide;

   • the $(k \geq n)$-morphisms are those of $Y$.

   I hope I got this right now…

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 28th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexHave added it to the entry in a new section _[Constructions -- For strict omega-groupoids](http://ncatlab.org/nlab/show/Postnikov+system#ForStrictOmegaGroupoids)_.

   Have added it to the entry in a new section Constructions – For strict omega-groupoids.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 29th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexI gave _[[Postnikov tower]]_ an Idea-section

   I gave Postnikov tower an Idea-section

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJun 6th 2017
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added discussion of a concrete model for the relative Postnikov tower of a chain map of chain complexes, regarded as a map of Kan-complexes under the Dold-Kan correspondence, [here](https://ncatlab.org/nlab/show/Postnikov+system#ExamplesForChainComplexes)

   I have added discussion of a concrete model for the relative Postnikov tower of a chain map of chain complexes, regarded as a map of Kan-complexes under the Dold-Kan correspondence, here