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-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry 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 galois-theory 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 limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology natural 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 string string-theory subobject 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).
    • I noticed that an entry bifunctor was still missing, though requested by some existing entries. So I briefly added something.

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

      Anonymous

      v1, current

    • Describing the arrangements which have been made for funding of the nLab in collaboration with the Topos Institute. The page, linked to from the home page, is intended to be fairly general; specific requests for donations can be made elsewhere.

      v1, current

    • have created enriched bicategory in order to help Alex find the appropriate page for his notes.

    • Some tidying up and additions at simplex category, in particular a section on its 2-categorical structure, and more on universal properties.

      I’ve edited the definition to focus more on the augmented simplex category Δ a\Delta_a instead of the ’topologists’ Δ\Delta’, but I haven’t changed their names, because it seemed to me that that was the best way to keep everyone involved in the discussion at that page happy. (I also changed the ordinal sum functor from ++ to \oplus, after Tim’s suggestion.)

    • New sections at coring:

      • base extension of corings
      • morphisms in the 1-category of corings over variable base rings.
    • This article has a weird claim on top, highlighted in yellow (see the second line):

      Redirected from “local Langlands correspondence”.

      Note: local Langlands conjecture and local Langlands conjecture both redirect for “local Langlands correspondence”.

    • This is a bare list of references, to be !include-ed into relevant entries, such as at swampland and 24 branes transverse to K3, for ease of cross-linking and updating.

      I am taking the liberty of including a pointer to our upcoming M/F-Theory as Mf-Theory which has some details on a precise version of the conjecture and a proof (from Hypothesis H).

      v1, current

    • I have added at HomePage in the section Discussion a new sentence with a new link:

      If you do contribute to the nLab, you are strongly encouraged to similarly drop a short note there about what you have done – or maybe just about what you plan to do or even what you would like others to do. See Welcome to the nForum (nlabmeta) for more information.

      I had completly forgotton about that page Welcome to the nForum (nlabmeta). I re-doscivered it only after my recent related comment here.

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

      v1, current

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

      Anonymous

      v1, current

    • I started an article about Martin-Löf dependent type theory. I hope there aren't any major mistakes!

      One minor point: I overloaded $\mathrm{cases}$ by using it for both finite sum types and dependent sum types. Can anyone think of a better name for the operation for finite sum types?

    • Tim Porter added references to microbundle and I edited the formatting of the entry a bit

    • Removed the following discussion to the nForum:

      Zoran Škoda: But there is much older and more general theorem of Hurewitz: if one has a map p:EBp:E\to B and a numerable covering of BB such that the restrictions p 1(U)Up^{-1}(U)\to U for every UU in the covering is a Hurewicz fibration then pp is also a Hurewicz fibration. But the proof is pretty complicated. For example George Whitehead’s Elements of homotopy theory is omitting it (page 33) and Postnikov is proving it (using the equivalent “soft” homotopy lifting property).

      Todd Trimble: Yes, I am aware of it. You can find a proof in Spanier if you’re interested. I’ll have to check whether the Milnor trick (once I remember all of it) generalizes to Hurewicz’s theorem.

      Stephan: I wonder if this trick moreover generalizes (in a homotopy theoretic sense) to categories other that Top\Top; for example to the classical model structure on CatCat?

      diff, v7, current

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

      v1, current

    • Added some basic examples from HTT. There doesn’t seem to be a page for the corresopnding 1-categorical notion. This notion is used pretty heavily in \infty-category theory, but it’s not so familiar from 1-category theory. But I’d have to think a 1-categorical treatment exists somewhere, right?

      diff, v2, current

    • (This is my first foray into nLab, so sorry if I'm making elementary errors.)
      In the definition of left adjoint of a functor U:C→ D, the claim is that it's a functor F:D → C s.t. ∃ natural transformations
      ι:id_C → F;U
      ϵ:U;F → id_D
      But F;U is a morphism in D and U;F is a morphism in C.
      Is something wrong here, have I misunderstood the notation F;U, is there a more general version of a natural transformation being used here, or what?
      Thank you.
    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • Mention relevance to (bo, ff) factorization system.

      diff, v6, current

    • The entry unit of an adjunction had a big chunk of mixed itex+svg code at the beginning to display an adjunction. On my machine though the output of that code was ill typeset. So I have removed the code and replaced it by plain iTex encoding of an adjunction.

      (Just in case anyone deeply cares about the svg that was there. It’s still in the history. If it is preferred by anyone, it needs to be fixed first.)

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

      Anonymous

      v1, current

    • starting something, not done yet

      v1, current

    • Idea-section and one further reference at Thomason model structure.

      I remember Mike once said on the blog somewhere that there might be some problem with Thomason's original claim that cofibrant objects in this structure are posets. I made a brief remark on this, but I can't find Mike's original comment.

    • Just started and I’m called away, but I’ll save anyway.

      v1, current

    • Created an entry for this.

      I’ve adopted the existing convention at nLab in the definition of Tw(C)Tw(C) (which is also the definition I prefer).

      Since the opposite convention is used a lot (e.g. by Lurie), I’ve decided it was worth giving it notation, the relation between the versions, and citing results in both forms. Since I didn’t have any better ideas, I’ve settled on Tw¯(C)\overline{Tw}(C).

      v1, current

    • I added the description of lax (co)limits of Cat-valued functors via (co)ends and ordinary (co)limits. I should probably flesh this out more.

      I’ve adopted the convention on twisted arrows at twisted arrow category, which is opposite of that in GNN.

      In the case of ordinary 2-category, when the diagram category is a 1-category, is the expression of lax (co)limits via ordinary weighted (co)limits really as simple as taking the weights C /C_{\bullet/} or C /C_{/\bullet}? I can’t find a reference that spells that out clearly; if there really is such a simple description it should be put on the lax (co)limit page.

      diff, v2, current

    • some bare minimum, for the moment just a glorified list of references

      v1, current

    • starting something – not done yet

      v1, current

    • Added material to injective object, including a proof of Baer’s criterion for injective modules, and the result that for modules over Noetherian rings, direct sums of injective modules are injective.

    • To record an article, I began this page.

      v1, current

    • Added link to Geoffrey Lewis’s 1974 thesis (under Kelly) “Coherence for a Closed Functor”

      diff, v18, current

    • this is a bare list of references, to be !include-ed as a subsection in the References-sections of relevant entries

      v1, current

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

      v1, current

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

      v1, current

    • Hello, I thought that a new entry would be a good thing. Just a sketch for now.

      v1, current

    • added to quantum anomaly

      • an uncommented link to Liouville cocycle

      • a paragraph with the basic idea of fermioninc anomalies

      • the missing reference to Witten’s old article on spin structures and fermioninc anomalies.

      The entry is still way, way, stubby. But now a little bit less than a minute ago ;-