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.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 24th 2017
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI started a page on a recent preprint, [[categorified Dold-Kan correspondence]].

   I started a page on a recent preprint, categorified Dold-Kan correspondence.

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 25th 2017
   • (edited Oct 25th 2017)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexSince this paper is taking initial steps to work out a categorified homological algebra and a categorified cohomology, is it time to categorify the [[cosmic cube]]? Are we entering a world where categorified cohomology concerns morphisms in an $(\infty, 2)$-topos? Maybe the [stratified homotopy hypothesis](https://ncatlab.org/nlab/show/poset-stratified+space#exit_path_categories) becomes salient here, so that 'striation sheaves' are geometric models for $(\infty, 1)$-categories with a fundamental exit path $(\infty, 1)$-category.

   Since this paper is taking initial steps to work out a categorified homological algebra and a categorified cohomology, is it time to categorify the cosmic cube?

   Are we entering a world where categorified cohomology concerns morphisms in an $(\infty, 2)$-topos? Maybe the stratified homotopy hypothesis becomes salient here, so that ’striation sheaves’ are geometric models for $(\infty, 1)$-categories with a fundamental exit path $(\infty, 1)$-category.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeOct 25th 2017
   • (edited Oct 25th 2017)
   • PermaLink
   Author: Urs
   Format: MarkdownItexWould be good to add to _[[categorified Dold-Kan correspondence]]_ a comment on how it is motivated by and subsumes and maybe sheds new light on various versions of the Waldhausen S-contruction, as Tobias Dyckerhoff explains in his introduction. (Myself no time.)

   Would be good to add to categorified Dold-Kan correspondence a comment on how it is motivated by and subsumes and maybe sheds new light on various versions of the Waldhausen S-contruction, as Tobias Dyckerhoff explains in his introduction.

   (Myself no time.)

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 25th 2017
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexSomething along those lines now there.

   Something along those lines now there.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeOct 25th 2017
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks!!

   Thanks!!

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeOct 25th 2017
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have also added a pointer under "related entries" at _[[categorification]]_. (That entry, of all entries here, is lacking some love. What about the ancient query box there? I think we can remove this and instead leave a coherent message.)

   I have also added a pointer under “related entries” at categorification. (That entry, of all entries here, is lacking some love. What about the ancient query box there? I think we can remove this and instead leave a coherent message.)