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 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

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

11581 to 11640 of 15078

  1. <
  2. 1
  3. ...
  4. 190
  5. 191
  6. 192
  7. 193
  8. 194
  9. 195
  10. 196
  11. 197
  12. ...
  13. 252
  14. >

    • I need to be able to point to linear differential equation, and so I created a minimum entry for this.

      Notice that at D-module is missing discussion that these model linear differential equations, but I don’t have the leisure now to do anything about this.

    • I have created an entry-for-inclusion

      in order to collect notation and terminology for plane (relativistic) waves (as a glorified “related concepts”-section); and so I am including this now into the relevant entries.

      In the course of this I created stubs for speed of light, Compton wavelength and dispersion relation redirecting energy-momentum relation, but no substantial content yet in any of these stub entries.

      I’ll go next and harmonize Fourier transform with this.

      (Previously I had had the ambition there to stick with the convention where the “2π2\pi” is in the exponents, instead of in the global prefactors; but I feel now that this is just too different from established practice, and I’ll change it.)

    • needed to be able to point to wave vector, so I created a bare minimum entry

    • needed to be able to point to plane wave, so I created a bare minimum entry

    • the entry valuation would deserve more clarification on that issue alluded to under “Sometimes one also…” and where the min-style definition appears the max-style definition should also appear.

      The entry should say that at least with some qualification added, then a valued field is a normed field with multiplicative norm. – Or should it be semi-normed?

      I could fiddle with it, but I feel I don’t quite get why the terminology here is so non-uniform that I am afraid I am missing something and maybe a more expert person should help.

      In Scholze 11, remark 2.3 is a useful comment:

      The term valuation is somewhat unfortunate: If Γ=ℝ ≥0\Gamma = \mathbb{R}_{\geq 0}, then this would usually be called a seminorm, and the term valuation would be used for (a constant multiple of) the map x↦−log|x|x \mapsto - log {\vert x \vert}. On the other hand, the term higher-rank norm is much less commonly used than the term higher-rank valuation.

    • Intending to write something on Fourier transforms of products of functions, I realized that “convolution product” used to redirect to group algebra, where only the discrete version of the concept was mentioned, and only hidden in a remark somewhere.

      As a first step, I have removed the redirect now and created with convolution product a disambiguation entry that indicates the general idea and mentions some classes of examples.

      Could be expanded much further.

    • since in other entries I keep having the need to directly point to it, I created a brief entry non-singular distribution.

      The only proposition there currently is (here) the density of the embedding C cp ∞(ℝ n)↪𝒟′(ℝ n)C^\infty_{cp}(\mathbb{R}^n) \hookrightarrow \mathcal{D}'(\mathbb{R}^n). I should find a canonical citation that also C ∞(ℝ n)↪ℰ′(ℝ n)C^\infty(\mathbb{R}^n) \hookrightarrow \mathcal{E}'(\mathbb{R}^n) is dense.

    • All our entries which wanted to point to something like dualizing module (such as at Verdier duality) or the more general concept in a closed monoidal category (such as at star-autonomous category) used to point to the entry dualizable object, which however did not really discuss this specific concept of “dualizable object”.

      Therefore I have now created dualizing object in a closed category and made these entries point to that, instead.

      Mentioned that in homological algebra/stable homotopy theory one usually puts additional finiteness conditions on the would-be dualizing object and added a brief remark on Anderson duality as a fundamental example.

    • I note that there is a page on codiscrete groupoid and a page on indiscrete category. As they were they did not link to each other. I have added some links, but perhaps some additional remarks on the terminology would be useful.

    • while I was adding more references and pointers to KR-theory I have created a brief stub for real algebraic K-theory, just to record the (still unpublished…?) references

    • I have split off a simple entry sphere bundle from spherical fibration in order to allow more precise linking (for instance from Thom space and from wave front set): “sphere bundle” is about fiber bundles whose fibers are isomorphic to spheres, while “spherical fibrations” is about those whose fibers have the (stable) homotopy type of spheres.

    • Often when typing “sub-anything” into some nnLab entry, I hesitate, wondering if this should come with a hyperlink. Maybe in general this is overkill, but right now, after creating unit sphere bundle, I felt like creating a simple entry sub-bundle, just for completeness.

    • Made a start at coordination. I’m unsure whether it’s worth spending too long on the intricate accounts of Schlick and Reichenbach, and then of whose makes best sense of Einstein’s proposals. Then there’s plenty of recent literature on the subject.

      For me, it would probably only be worth expanding if we could thrash out an account of what the nPOV has to say on the subject. Urs has suggested we look at Bohrification. That sounds like the best lead. Reading through the Bohr topos entry, however, it seemed to me that little is said there about how to integrate that with other parts of the synthetic QFT story. There’s the idea of the ’fifth axiom’, but shouldn’t we expect these quantum phase spaces to have appeared earlier as part of the quantization process. Or do we see it merely as way to interpret our way back from the weird quantum world to something as classical as possible so as to be able to relate theory to the recordings of our classical instruments?

    • I would like to start a page on descriptive complexity. Complexity theory is an area of research in computer science that aims to determine the amount of resources (time and space usually) that an algorithm needs to decide a problem. Descriptive complexity is a branch of complexity theory that uses finite model theory (first-order, second-order, and some in-between operators) to describe the problems. It turns out that these languages directly corresponds to known complexity classes.

      My aim is to translate the logic used into an equivalent topos theory of finite logic, or even do away with logic altogether and directly map complexity classes with a corresponding category. The goal of this is to reframe questions in complexity theory as questions in category theory.

      For example: we can describe the existential second order quantifier as the left adjoint of the diagonal functor (context extension?) from $P(P(X)) \to P(P(X))\times P(P(X))$. I'm not sure whether $X$ is the ccc with all the propositional formulas, or if it's the finite model. I'm still learning.

      Would it be appropriate to add to the nLab? I'm autodidactic with category theory, so I'm not sure if I can accurately describe things, but I'd still like a space to share my ideas.

    • I have expanded a bit at Serre-Swan theorem: gave it an actual Idea-section, mentioned more variants (over general ringed spaces, in higher geometry) and added more references.

    • I have started an entry on shuffles. It is meant to be an ’elementary introduction’ so there will be room for deeper exploration of them in follow-on entries.

    • I wrote the article distribution. I'm by no means an expert though. I left open a section "Applications" in case someone would like to add some, or if not I'll try to fill this in soon.

    • Created a stub tangent bundle categories as a link target to be disambiguated from tangent categories (with a hatnote at the latter). What I’m calling “tangent bundle categories” here are usually called just “tangent categories”, but that clashes with our page tangent category, so I invented a variation. Better suggestions are welcome.

    • Started bornological set. Some people call it a bornological space, but that conflicts with the terminology in functional analysis which refers to a locally convex TVS with a suitable “bounded = continuous” property. I quickly wrote that uniformly continuous maps between metric spaces induce bounded maps, but I’ll recheck when I have a free moment.

    • Needed to be able to point to contractible chain complex and discovered that we didn’t have an entry for that, so I quickly created one.

    • I gave Koszul complex and Idea-section and stated two key Properties in citable form (but without proof), one of them the statement that a sufficient condition for the Koszul complex to be a resolution of R/(x 1,⋯,x n)R/(x_1, \cdots, x_n) is that RR is Noetherian, the x ix_i are in the Jacobson radical, and the cohomology in degree -1 vanishes.

      Finally I stated the special case of this (here) where RR is a formal power series algebra over a field and the elements x ix_i are formal power series with vanishing constant term.

      (I have added the relevant facts as citable numbered examples at Noetherian ring and at Jacobson radical.)

      This happens to be the case that one need in BV-formalism in field theory. I am writing this out now at A first idea of quantum field theory (here).

    • I tried over category and found the arrows (and a lot else) were not showing up. (On Firefox 56.0, and on Chrome and Safari)

      This is after discovering that the accents on Myles Tierney were not appearing. Strangely they do appear at Alain Prouté, (perhaps they are a different font????)

    • The IAS has an article by Voevodsky. I have given a link in the article on him.

    • Arnold Neumaier contacted me about the previous stubbiness of the entry resurgence and pointed me to his PO comment on the topic (here). I have put that into the Idea-section of the entry, equipped with some links.

    • on my personal web I am starting a page derived critical locus (schreiber) with some notes.

      I think so far I can convince myself of the claim that the page currently ends with (without proof). My next goal is to show that the homotopy fibers discussed there are given by BV-BRST complexes. But I have to interrupt now.

    • I have seen filtered object also used in settings where there may not be an ∅\emptyset (or initial object) and where the filtration can be doubly infinite. In the current entry both seem not to be allowed. Is this deliberate with another term being used for the more general concept?

    • New entry (improvized, check co- etc.) resolution.

    • I couldn’t find an existing discussion for this page – I hope I’m not duplicating such an existing discussion.

      I just added a bit to the introduction to clarify something that I was confused about – a cartesian bicategory basically abstracts the properties of V-Prof, but only for cartesian V. To me, this feels like an interesting intermediate position between abstracting the properties of V-Prof for general V, and abstracting the properties of a bicategory like Cat.

      Of course, feel free to correct, rework, or roll back entirely my additions! Todd in particular has clearly put a lot of work into this page already.

    • I had need to point specifically to ideals in Lie algebras, so I gave them a little entry Lie ideal.

11581 to 11640 of 15078

  1. <
  2. 1
  3. ...
  4. 190
  5. 191
  6. 192
  7. 193
  8. 194
  9. 195
  10. 196
  11. 197
  12. ...
  13. 252
  14. >
Top of Page