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 beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science connection constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality education elliptic-cohomology enriched fibration foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck 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 infinity integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monad monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar 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-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).
    • added to measure space a link to measurable locale.

      In the course I notice the following remnant discussion, which hereby I move from there to here


      Eric: Some day this should hopefully tie into the beautiful stuff on Leinster measure (blog).

      +– {: .query} Eric: dd is also the exterior derivative and dμd\mu is a volume form. Is there a nice way to say this that is consistent with the above? Update: The Usenet discussion probably discusses this, but I’m too lazy to read the whole thing right now (past my bedtime!).

      Toby: As a volume form is not, in general, the exterior derivative of anything, you cannot interpret the ‘d\mathrm{d}’ in (eq:excessive) as an exterior derivative. You can do this for the ‘d\mathrm{d}’ in (eq:Leibniz), of course, because that is on the real line, where the volume form is the exterior derivative of the identity function (xx)(x \mapsto x). But in general, an absolutely continuous Radon measure μ\mu on an oriented smooth nn-dimensional manifold XX defines an nn-form on XX (and vice versa), so if you call the form μ\mu as well, then you want to use (eq:simple). (The exterior deriviative of the volume form, of course, would be zero!)

      I'm actually halfway through writing an article differential form where I will address some of this. (I guess that I'm going through old Usenet posts of mine; I am using the conversation that you and I had with John in this old thread as reference for some of it!)

      Eric: I look forward to it! By the way, that Usenet discussion was a nice blast from the past :)

      Eric: I put some comments about that discussion here.

      Toby: I should note that, even given what I wrote above, there is still a slight clash of notation between measure theory and differential topology. To fix this, the dx\mathrm{d}x in (eq:full) could be replaced with |dx||\mathrm{d}x|. This has to do with the whole the-absolute-value-of-an-nnform-is-an-nnpseudoform and integration-of-nnpseudoforms-is-more-fundamental-than-integration-of-nnforms issue. I referred to this clash of notation in our Usenet conversation here.

      Eric: It’s starting to come back to me now. Yeah, the measure is really a pseudo nn-form and we settled on the notation |dx||dx| for that. We should at least give a nod to that idea I think in the above.

    • Gave an explicit definition as the quotient ring A[x]/(ax1)A[x] / (ax - 1), and mentioned the equivalent definition in terms of multiplicative systems. Gave the example of Laurent polynomials. The explicit definition was already given at localisation of a commutative ring, but the multiplicative system was not given, and I think the construction is fundamental enough to warrant its own page. I will tweak localisation of a commutative ring to link to the new page.

      v1, current

    • am starting something, but not done yet, nothing to be seen here for the moment

      v1, current

    • Fixed typo in Definitions section

      Anthony Hart

      diff, v3, current

    • am starting some minimum here. Have been trying to read up on this topic. This will likely become huge towards beginning of next year

      v1, current

    • added pointer to

      • Stefano Frixione, Benjamin Fuks, Valentin Hirschi, Kentarou Mawatari, Hua-Sheng Shao, Marthijn P. A. Sunder, Marco Zaro, Automated simulations beyond the Standard Model: supersymmetry (arXiv:1907.04898)

      diff, v11, current

    • Added formatting, hyperlinks, toc and floating-toc.

      But mainly I came here to see if decidable inclusion should redirect here (which is now required at constructive model structure on simplicial sets). I have made it a redirect, but there is much room in this and related entries for experts to live out their expertise

      diff, v4, current

    • I am writing an exposition (or a dictionary) integral transforms on sheaves.

      Check it out. I will have to go offline soon. Maybe somebody feels like further polishing/expanding this up a bit. Then later I want to supply that for the current nnCafé discussion.

    • I fixed a broken link to Guy Moore’s lectures

      diff, v9, current

    • Todd,

      you added to Yoneda lemma the sentence

      In brief, the principle is that the identity morphism id x:xxid_x: x \to x is the universal generalized element of xx. This simple principle is surprisingly pervasive throughout category theory.

      Maybe it would be good to expand on that. One might think that the universal property of a genralized element is that every other one factors through it uniquely. That this is true for the generalized element id xid_x is a tautological statement that does not need or imply the Yoneda lemma, it seems.

    • entry renamed to fit more systematic naming pattern

      diff, v29, current

    • Some stuff that Zoran wrote on recollement reminded me that I had been long meaning to write Artin gluing, which I’ve done, starting in a kind of pedestrian way (just with topological spaces). Somewhere in the section on the topos case I mention a result to be found in the Elephant which I couldn’t quite find; if you know where it is, please let me know.

    • a stub, on occasion of today’s

      and to provide the previously missing link at flavour anomaly for

      • David Marzocca, Addressing the B-physics anomalies in a fundamental Composite Higgs Model, JHEP07(2018)121 (arXiv:1803.10972)

      v1, current

    • I’m not sure that the definition on this page is correct. Despite how wrong it seems to a category theorist, I think the adjective “complete” in “cpo” usually refers only to a countable sort of completeness. According to wikipedia, a “cpo” can mean at least three different things dependent on context, but “never” a partial order that’s actually complete as a category (i.e. a complete lattice).

      diff, v3, current

    • a stub, for the moment just so as to record references

      v1, current

    • changed page name to make it fit more systematic naming pattern

      diff, v25, current

    • Reading the blog entry

      and the reactions to it made me realize that apparently there is no comprehensive list either in print or online of all the insights into QFT in general and observed standard model physics in particular, that have been obtained via results in string theory.

      So I have entertained myself with starting to collect notes for such a list:

      In the process I have created a bunch of new entries, most of them stubs, linked to from there.

    • at KLT relations I have expanded the list of references. I added also references for the generalization of these relations that is known these days as “gravity is Yang-Mills squared” or similar (eventually this might want to be a separate entry).

      In this course I also expanded the list of references at quantum gravityAs a perturbative quantum field theory

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

      v1, current

    • I noticed that augmented simplicial set did not point anywhere, so i created the entry. But have no energy to put anything of substance there right now.