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    • 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=0, then this would usually be called a seminorm, and the term valuation would be used for (a constant multiple of) the map xlog|x|. 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 Ccp(n)𝒟(n). I should find a canonical citation that also C(n)(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 nLab 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 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/(x1,,xn) is that R is Noetherian, the xi are in the Jacobson radical, and the cohomology in degree -1 vanishes.

      Finally I stated the special case of this (here) where R is a formal power series algebra over a field and the elements xi 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 (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.

    • tried to polish and improve the floating TOC

      higher algebra - contents

      The entry higher algebra itself I am not happy with (well, it’s mostly just a link list). But no time for that right now.

    • I have created an entry transgression of differential forms that discusses the concept using the topos of smooth sets. Apart from the traditional definition as τΣΣev* the entry considers the formulation as

      τΣ=Σ[Σ,]

      which simply forms the internal hom into the classifying map XΩn of a differential form. I have spelled out the proof that the two definitions are equivalent.

      Then the entry contains statement and proof of the situation of “relative” transgression over manifolds with boundary. (This is what yields, when applied to Lepage forms, Lagrangian correspondences between the phase spaces with respect to different Cauchy surfaces, which is what I currently need this material for in the exposition at A first idea of quantum fields.)

      Finally there are two examples, a simplistic one and an simple but interesting one related to Chern-Simons theory. These two examples I had kept for a long time already at geometry of physics – integration in the section “Transgression”. That section I have now expanded accordingly, its content now coincides with the entry transgression of differential forms.

    • I have added in some additional comments plus some references. In particular there is a paper by Barbara Osofsky (The subscript of n projective dimension, and the vanishing of lim(n)_, Bull. Amer. Math. Soc. Volume 80, Number 1 (1974), 8-26.) which gives a neat discussion.

    • I have added to causal complement the actual definition of causal complements of subsets of Lorentzian manifolds.

      The entry used to contain only a more abstract concept, now kept as the second subsection of the Definition section here.

    • It is a classical fact that a formal deformation quantization of a Lie-Poisson structure is provided by the universal enveloping algebra of the corresponding Lie algebra. Remarkably, this statement generalizes to some extent to more general (polynomial) Poisson algebras. In particular it holds for every such up to degree three in ! This is due to Penkava-Vanhaecke 00.

      I have added a quick summary of this theorem to deformation quantization in a new subsection: Existence – Deformation by universal enveloping algebras. I also gave this an entry on its own at polynomial Poisson algebra.

      This is maybe remarkable, since there is possibly no physical measurement known which could detect contributions of higher than third order in . Though I’d need to check. This is subtle because order in is different from the usual loop order that is commonly stated (which is order in the coupling constant) and the relation between the two is complicated.)

      Also (and that’s how I came across this article) at least in special cases this gives a way to quantize just by universal constructions on Lie algebras, hence this might potentially tell us something about the quantization of Poisson bracket Lie n-algebras (for which no analog of the corresponding Poisson algebra, i.e. with an associative product around, is known).

    • I have added a brief entry causal locality in order to have somethign to point to when discussing the corresponding axiom at local nets of observables (the latter entry I am about to brush up and expand)