Not signed in (Sign In)

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 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

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).

nLab > Latest Changes

Show all

12661 to 12720 of 14392

  1. <
  2. 1
  3. ...
  4. 208
  5. 209
  6. 210
  7. 211
  8. 212
  9. 213
  10. 214
  11. 215
  12. ...
  13. 240
  14. >

    • Someone, apparently in Berlin, has created a page called www.mfo.de/document/1145/OWR_2011_52.pdf, with just that text (and ’My First Slide’) in the body. The URL points to a report on a logic workshop at Oberwolfach around this time last year. It’s not spam, but what should we do with it?

    • Someone signing themselves as ‘Joker? at November 3, 2012 08:05:13 from 93.129.88.58’ deleted two lines from sheaf and topos theory. There seemed no reason for this, so I have rolled back to the previous version.

    • The recent changes to the various modal logic pages have changed the emphasis from the ’many agent’ versions S4(m)S4(m).etc. to a type theoretic one. That would be okay but in so doing they have become a bit garbled so they refer to K(m) but then just describe KK itself. I am wondering what is planned for these. I originally wrote them with the aim of increasing the nPOV side of the Computer Science entries and to have some brief introduction to modal logs, what should they become?

    • October 24, 2012 09:26:08 by Anonymous Coward (99.133.144.164) has added a comment questioning the validity of a sentence at reflective subcategory.

    • wanted to be able to say sum and have a pointer to somewhere.

    • I made starts on lexicographic order and on compactification. Lexicographic order was defined only for products of well-ordered families of linear orders (probably the most common type of application).

      I’m not very happy with the opening of compactification.

    • I edited the old entry projection a little.

      There is no real systematics in common use of “projection” as opposed to “projector”, but I think the following makes good sense:

      1. a projection is a canonical map out of a product;

      2. a projector is an idempotent in a suitably abelian category

      and then the relation is: A projector is a projection followed by a subobject inclusion.

      That’s how I have now put it in the entry.

    • New entry enumerative geometry. New stubs Schubert calculus, intersection theory.

      By the way (Andrew); the title of this nForum post is not seen but truncated. This happens because of some other stuff is placed into the corner in the same line. It says unimportant info “Bottom of Page” preceded by long space between the truncated title and this info ad. I think it is more important that the titles be spelled entirely.

    • created a table of contents idempotents - contents and included it as a floating TOC into the relevant entries

    • While writing at k-morphism, I noticed there is no article on globular operad (aka Batanin operad), so I wrote one. Experts please look over, and improve if desired.

    • While writing the new Idea-section now at Segal condition I felt the need to have a table of contents

      So I started one and added it to the relevant entries as a floating TOC.

    • I think we need a floating table of contents categories of categories - contents to connect our entries on related topics. I have started one.

      But this needs to be further expanded. also haven’t included it into the relevant entries yet, no time right now.

    • I have written out in some detail the proof at Grothendieck spectral sequence.

      But I still need to go through it and proof-read and polish. Handle with care for the moment. Maybe the whole thing needs to be rearranged, for readability.

    • I (only) now realize that I pretty much missed the story of familial regularity and exactness. But also it was easy to miss, with the entries that are unified by this not pointing back to it.

      To rectify this I have created now a floating TOC and am including it into all the relevant entries:

      Please check out that TOC and edit/modify as need be.

    • I've done a tiny bit of work to add a more intuitive introduction to the concepts of model category and Quillen equivalence, and I plan to do some more. If anyone wants to help, that would be great. For example, it would be nice to give some general intuition for fibrations, cofibrations and weak equivalences and why they matter.

    • slightly restructured, added table of contents and then added remarks to cobordism hypothesis (in the section "remarks") using material from blog discussion over at SecretBloggingSeminar.

    • I did some editing over at free module, under the section on submodules of free modules. I don’t have Rotman’s book before me, so I can’t check whether he assumes the commutativity hypothesis for proposition 2, but I put it in to be safe. (Actually, I’ll bet it’s needed, since we have to be careful around invariant basis number which holds for commutative rings.) The proof that I added does use this hypothesis.

      Also, I deleted the remark that this is the Nielsen-Schreier theorem in the case R=ℤR = \mathbb{Z}, since NS refers to groups as opposed to abelian groups.

    • created an entry titled Topological Quantum Field Theories from Compact Lie Groups

      on the recent (or not so recent anymore) article by Freed-Hopkins-Lurie-Teleman (therefore the capizalization).

      I typed into this a summary of their central proposal for how to formalized the path integral quantization for "direcrete" quantum field theories, in terms of higher category theory.

      I think this is important, and is actually a simple idea, but few people having looked at the article maybe get away with the take-home message here. So I tried to amplify this.

      I also have some own thoughts about this. So I put a big query box in the end, with a question.

    • At principal ideal domain, I stated and proved the theorem that for modules over a pid, submodules of free modules are free (assuming the axiom of choice), and gave a couple of corollaries. This is at the head of a section on the structure theory of modules, which obviously could be expanded to treat the structure theory of finitely generated modules over a pid.

    • Copying old query box here from pseudofunctor (having incorporated its content into the entry):

      Tim: in specifying a pseudo functor FF you have to decide whether the isomorphism goes from F(gf)F(g f) to F(g)F(f)F(g) F(f) or in the other direction. Of course they are equivalent as each will be inverse to the other. You might say that one is lax and pseudo the other op-lax and pseudo. When specifying the Grothendieck construction for such a functor, which is to be preferred?

      Both are about equally represented in the literature that I have seen which gets confusing. (In other words, I’m confused!)

      Toby: As you suggest, the two versions are equivalent, so in a way it doesn't make a difference. But it might be nice to settle a convention in case we need it.

      Tim: I have been using (for the Menagerie) the idea that there are pseudofunctors presented in two equivalent flavours lax pseudofunctor and oplax ones.

      Mike: Well, the natural comparison maps that you get in a Grothendieck fibration go in the “lax” direction F(g)F(f)→F(gf)F(g) F(f) \to F(g f), since they are induced by the universal property of cartesian arrows. In particular, if you have a functor with “weakly cartesian” liftings that don’t compose, then it is a lax functor. Not a very strong argument, but if we just want some convention it might be a reason to pick lax. I think that making too big a deal out of the difference would be misleading, though.

    • D-geometry and Riemann-Hilbert problem. In order to make more visible one of the principal directions, where the series of entries which I am writing these days is heading to.

    • I created adequate subcategory. However, once I’d done so then I found it linked from dense functor and after reading that I wasn’t sure I ought to have created the original page. I did so because I wanted to record Isbell’s idea as it’s fairly relevant to categories of generalised smooth spaces - the test spaces form an adequate subcategory (or sort of do, I need to work out the details).

      It seems to be old terminology (reading dense functor) so maybe a page devoted to it isn’t right. I could shift it to dense functor?

    • Maybe I am looking at the wrong places: is there somewhere a discussion of examples for classes of toposes that satisfy COSHEP?

      What is known about which sites induce toposes that validate COSHEP?

    • Extended the entry Cohn localization now starting with the ring viewpoint. Urs: I hope you will now agree that it is justified to call it a localization of a ring R→Σ −1RR\to \Sigma^{-1} R.

    • On some pages it is desireable to have cardinalities “ℵ\aleph” be provided with a link to their explanation. I have cerated a redirect-page ℵ for that purpose.

    • I started creating the following tables for the entry geometry of physics. After having created them there I found that these deserve to be put into the related entries, too. So therefore I put them into their own pages now and included them in related entries via

        [[!include .... - table]]

      These are the tables that I have so far:

      These need a bit mor attention. But I have to quit now for the time being. Also, I am afraid I may be running here again against Mike’s preference for notation here and there.

      But I am not dogmatic about this, I just created these tables as they happened to occur to me. I try to polish them later.

    • at variational calculus I have started a section In terms of smooth spaces where I discuss a bit how for

      S:[Σ,X] ∂Σ→ℝ S \colon [\Sigma, X]_{\partial \Sigma} \to \mathbb{R}

      a smooth “functional”, namely a smooth map of smooth spaces, its “functional derivative” is simply the plain de Rham differential of smooth functions on smooth spaces

      dS:[Σ,X] ∂Σ→Sℝ→dΩ 1. \mathbf{d}S \colon [\Sigma, X]_{\partial \Sigma} \stackrel{S}{\to} \mathbb{R} \stackrel{\mathbf{d}}{\to} \Omega^1 \,.

      The notation can still be optimized. But I am running out of energy now. Has been a long day.

    • (Edited.) An anonymous poster has created a page with Vesselin’s comments on MO simply copied and pasted. I don’t know what others think of this, but whether this is an appropriate use of the nLab seems open to debate. What do others think?

    • I created a page Lax equation having no content so far but soon there will be some content.

    • I just have met Jamie Vicary in Brussels, at QPL 2012. In his nice talk he pointed to an nnLab page which I didn’t know existed:

      It’s about a computer algebra software that can handle KV-2-vector spaces. I have just now added some cross links.

    • I have worked on the general structure of the entry locally presentable category. The previous structure was a bit erratic at times, due to the way it had grown. I have tried to collect paragraphs by topic, give them numbered environments, move theorems from the Examples-section to the Properties-section and so forth.

    • Something odd has been happening at a new entry entitled exchange structure. Someone signing in as Carol entered in quite a lot of material relating to J. Ayoub, Les six opérations de Grothendieck et le formalisme des cycles évanescents dans le monde motivique. This has just been deleted from the same IP address. This probably means nothing important but it is worth noting.

    • I wanted to be able to point to practical foundations more directly than pointing to foundations and hoping that the reader would spot the paragraph on practical foundations there. So I split off an entry practical foundations. For the moment it contains nothing but the relevant material from foundations copy-and-pasted

    • since I needed to point to it explicitly, not just via the entry BRST complex, I have created an entry ghost field with a paragraph of text.

      I promise that one day I fill in more detailed discussion, but not right now.

    • created metric jet after a mention at the Café.

    • there already was a bit of case distinction at functional between the notion in functional analysis and the nonlinear notion in mapping space theory. I have edited a bit more, trying to polish a bit.

    • Ross Tate has pointed out a mismatch in terminology: Kleisli objects and the Grothendieck construction (of a covariant Cat-valued functor) are both asserted to be “lax colimits”, but they are not the same kind of colimit (the 2-cells go in different directions). Thinking about this more, I have concluded that Kleisli objects are lax colimits and the Grothendieck construction is an oplax colimit. I wrote a bit about my reasoning here. But before I go changing all references to the Grothendieck construction to say “oplax colimit”, I thought I should do a sanity check — does this make sense to everyone else?

12661 to 12720 of 14392

  1. <
  2. 1
  3. ...
  4. 208
  5. 209
  6. 210
  7. 211
  8. 212
  9. 213
  10. 214
  11. 215
  12. ...
  13. 240
  14. >
Top of Page