Not signed in (Sign In)

Start a new discussion

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-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus 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 homology 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 monads monoidal monoidal-category-theory morphism motives motivic-cohomology newpage nforum nlab noncommutative noncommutative-geometry number-theory object 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 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).
    • am giving this its own little entry, since there are several entries that need to refer to this statement, so that it’s good to have a single place where to collect all the cross-links and references (of which I have only one, for the moment)

      v1, current

    • Prop. 2.13 “stable” should be “strict”


      diff, v40, current

    • Created a stub for cofunctor? with some references.

      v1, current

    • edited decalage a bit

      there was the statement that  Dec Y \to Y is a "fibration". I made that Kan fibration. Is that right?

    • there was a pointer to the generalization of “faithful functor” to 2-categories. I have added below that pointer to the corresponding version for (,1)(\infty,1)-categories.

      diff, v11, current

    • I need a word for the homotopy quotient (X)/S 1(\mathcal{L}X)/S^1 of free loop spaces X\mathcal{L}X by their canonical circle action. It seems that the only term in use with respect to this is “twisted loop space”, which however usually refers just to the constant loops ( constX)//S 1(\mathcal{L}_{const}X)//S^1. Since under nice conditions the derived functions on the Spec(A)/S 1\mathcal{L}Spec(A)/S^1 is the cyclic homology complex of AA, I suggest that a good name is “cyclic loop space”. I made a quick note at cyclic loop space, just to fix and disambiguate terminology.

    • starting something, not done yet

      v1, current

    • Created stub to clear grey link.

      v1, current

    • Added remark on geometric realizations of pairs of adjoint functors

      Roman T

      diff, v17, current

    • made some minor cosmetic edits, such as replacing

        \bar W G

      (which comes out with too short an overline) with

        \overline{W} G

      diff, v2, current

    • for the moment just to make links work

      v1, current

    • An attempt to create this page was made by Paulo Perrone, but the creation was not successful. Am creating the page without any content beyond ’TODO’ now as a test.

      v1, current

    • In the examples section of extensive category, it is stated that the category of affine schemes is infinitary extensive.

      For all I know, I was the one who stuck in that example. But is that statement actually true? I’m having trouble seeing it.

      If SS is a commutative ring over RR (by which I mean under RR (-:), does the functor S R:CAlg RCAlg RS \otimes_R -: CAlg_R \to CAlg_R preserve arbitrary cartesian products? Because it seems that’s what we basically need for the statement to be true.

    • Since it was mentioned by Urs on g+, I thought I’d start mysterious duality. Maybe not a great name when someone discovers how it works (as someone claims to have done here).

    • am giving this its own entry, for ease of hyperlinking. Made up the terminology, maybe there is a better choice.

      v1, current

    • Rewrote misleading comment seeming to imply wide pullbacks need to be preserved to get preservation of equalizers.

      Kevin Carlson

      diff, v13, current

    • Added the contents of the canonical isomorphism induced by some non-canonical isomorphism as coming from Lack’s proof.

      diff, v32, current

    • a bare sub-section with a list of references – to be !included into relevant entries – mainly at confinement and at mass gap problem (where this list already used to live)

      v1, current

    • starting something. Not done yet but need to save

      v1, current

    • Have added to cyclic set a pointer to notes from 1996 by Ieke Moerdijk where the theory classified by the topos of cyclic sets is identified (abstract circles).

      This is an unpublished note, but on request I have now uploaded it to the nLab

      • Ieke Moerdijk, Cyclic sets as a classifying topos, 1996 (pdf)

      I have also added a corresponding brief section to classifying topos.

      By the way, there is an old query box with an exchange between Mike and Zoran at cyclic set. It seems to me that this has been resolved and the query box could be removed (to make the entry read more smoothly). Maybe Mike and/or Zoran could briefly look into this.

    • Fixed pdf link to “Towards an understanding of Girard’s transcendental syntax”


      diff, v6, current

    • added the definition to cyclic homology

      next the task is to write out the details for how under the identification of the Hochschild complex with functions on the derived loop space, the cyclic complex is the S 1S^1-equivariant functions on the derived loop space.

    • I have begun cleaning up the entry cycle category, tightening up definitions and proofs. This should render some of the past discussion obsolete, by re-expressing the intended homotopical intuitions (in terms of degree one maps on the circle) more precisely, in terms of “spiraling” adjoints on the poset \mathbb{Z}.

      Here is some of the past discussion I’m now exporting to the nForum:

      The cycle category may be defined as the subcategory of Cat whose objects are the categories [n] Λ[n]_\Lambda which are freely generated by the graph 012n00\to 1\to 2\to\ldots\to n\to 0, and whose morphisms Λ([m],[n])Cat([m],[n])\Lambda([m],[n])\subset\mathrm{Cat}([m],[n]) are precisely the functors of degree 11 (seen either at the level of nerves or via the embedding Ob[n] ΛR/ZS 1\mathrm{Ob}[n]_\Lambda\to \mathbf{R}/\mathbf{Z}\cong S^1 given by kk/(n+1)modZk\mapsto k/(n+1)\,\mathrm{mod}\,\mathbf{Z} on the level of objects, the rest being obvious).

      The simplex category Δ\Delta can be identified with a subcategory of Λ\Lambda, having the same objects but with fewer morphisms. This identification does not respect the inclusions into CatCat, however, since [n][n] and [n] Λ[n]_\Lambda are different categories.

      diff, v27, current

    • added a reference to Dynamical Systems and Sheaves by Schultz, Spivak, and Vasilakopoulou

      Joe M

      diff, v8, current

    • Page created, but author did not leave any comments.

      v1, current

    • Created semi-simplicial set, mainly as a repository for some terminological remarks. I would welcome anyone more knowledgeable about the history to correct or improve it!

    • Page created, but author did not leave any comments.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • I have changed the title of this article, as well as references to the object within it. Use of the term “Hawaiian Earring” is objected to by Hawaiian mathematicians. Please see these two threads, one by native Hawaiian and math PhD Dr. Marissa Loving, and the other by an expert on the Hawaiian Earring, Dr. Jeremy Brazas.

      I have retitled the article “Shrinking wedge of circles”, which is the name used for this space in Hatcher’s “Algebraic Topology”. I have a retained a note in the body of the article that the space is sometimes referred to as the “Hawaiian earring space”.

      This small change in name helps to make mathematics a more inclusive and just field, especially in consideration of the historical marginalization and exclusion of indigenous mathematicians. By taking this action, the nLab site can help to spread a change in language more widely, including on other math reference sites.

      I hope that this change is readily accepted and approved by the nLab community. Thank you!

      Justin Lanier

      diff, v9, current

    • Finally noticed that this entry here was a stub without TOC, without references and without cross-links. Have touched it a little.

      diff, v4, current