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    • added these pointers:

      • Dam Thanh Son, Mikhail Stephanov: Relativistic Guiding-Center Motion: Action Principle, Kinetic Theory, and Hydrodynamics, Phys. Rev. Lett. 133 (2024) 145201 [arXiv:2405.08073, doi:10.1103/PhysRevLett.133.145201]

      • Dam Thanh Son: Lorentz-covariant description of relativistic guiding-center motion, talk at Simons Center Physics Seminar (2025-02-12) [webpage]

      (which may ultimately want to go to a more specialized entry, but for the moment I see no better place than to have them here)

      diff, v6, current

    • I included an abstract and preface (test for now!)

      IMustafaNasreddin

      v1, current

    • whart the glorpus??11?22???

      zxorvorp

      v1, current

    • creating a stub entry, for now just to make the link work, and to have a home for references specific to abelian CS

      v1, current

    • Some ×\times were written as xx, so fixed. There were sign changes going on that I didn’t understand, p 2−(12p 2) 2p_2 - (\frac{1}{2}p_2)^2 and p 2+(12p 1) 2p_2 + (\frac{1}{2}p_1)^2.

      diff, v45, current

    • Created.

    • Removed a query:

      +– {: .query} Bruce: I’m shooting in the dark here with this ω\omega-groupoid sentence above. Am I right? What does that boil down to concretely? =–

      +– {: .query}

      Bruce: What’s a geometric stack?

      Chris: A stack is geometric if it is quasi-compact (any open cover has a finite sub-cover) and the diagonal morphism is representable and affine, though that probably doesn’t help much. I don’t know much about stacks yet, but maybe someone else can explain this. I think the point is that one needs some hypotheses to actually prove stuff for stacks.

      =–

      diff, v70, current

    • At crossed module it seems we are missing what i think should be the prototypical example: the relative second homotopy group π 2(X,A)\pi_2(X,A) together with the bundary map δ:π 2(X,A)→π 1(A)\delta:\pi_2(X,A)\to \pi_1(A) and the π 1(A)\pi_1(A)-action on π 2(X,A)\pi_2(X,A). As someone confirms this example is correct I’ll add it to crossed module.

    • brief category:people-entry for hyperlinking references

      v1, current

    • added some actual content to the entry, so far on the idea of the quantum YBE.

      diff, v6, current

    • I have corrected the statement about the diagonal matrices forming the center: an additional condition is necessary, for example that the ring is an algebraically closed field (Schur lemma).

      diff, v8, current

    • There seem to be some misleading remarks at Čech model structure on simplicial presheaves.

      Accordingly, the (∞,1)-topos presented by the Čech model structure has as its cohomology theory Čech cohomology.

      Marc Hoyois seems to says the opposite: there is no deep relation between “Čech” in “Čech cohomology” and in “Čech model structure”.

      […] the corresponding Čech cover morphism .

      Notice that by the discussion at model structure on simplicial presheaves - fibrant and cofibrant objects this is a morphism between cofibrant objects.

      The Čech nerve is projective-cofibrant if we assume the site has pullbacks. I don’t know how to prove it otherwise. Of course, injective-cofibrancy is trivial.

      this question is evidently also relevant to what the correct notion of internal ∞-groupoid may be

      Based on the discussion here, it seems that the Čech model structure is not site-independent, even though it can be defined on the category of simplicial sheaves. A very strange state of affairs…

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinks references

      v1, current

    • possibly empty groups

      Anonymous

      v1, current

    • Added these pointers to today’s replacements:

      • Changha Choi, Leon A. Takhtajan: Supersymmetry and trace formulas I. Compact Lie groups [arXiv:2112.07942]

      • Changha Choi, Leon A. Takhtajan: Supersymmetry and trace formulas II. Selberg trace formula [arXiv:2306.13636]

      diff, v8, current

    • starting something, but nothing much here yet

      v1, current

    • briefly recording the way to isomorph linear representations of compact groups on Hilbert spaces into unitary reps, by group-averaging

      v1, current

    • a bare list of references, to be !included into the References-section of relevant entries, for ease of synchronizing (such as at anyon but also at vortex etc.)

      v1, current

    • I added some more to Lebesgue space about the cases where 1<p<∞1 \lt p \lt \infty fails.

    • Added a bunch of material to inverse semigroup under subsections of “Properties”.

    • I have added some discussion to variable.

      Not sure if I ever announced this here, the original version is a few months old already. But right now I have added also some sentences on bound variables.

      Some more professional logician might please look over this. There will be lots of room to improve on those few sentences that I jotted down, mainly such as to have something there at all.

    • have made explicit the statement that for a pair of adjoint (co)monads their EM-categories are isomorphic (now this Prop).

      Also tried to to give this entry a more systematic structure, but still some way to go.

      diff, v11, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • a stub, to make links work

      (This used to be a stub “quantum circuit” which I just quasi-duplicated at a more extensive entry quantum circuit diagram. But since quantum gate was already redirecting here – which is how I discovered/remembered that this entry exists – no harm is done by making that it’s new title.)

      diff, v4, current

    • I am trying to collect citable/authorative references that amplify the analog of the mass gap problem in particle phenomenology, where it tramslates into the open problem of computing hadron masses and spins from first principles (due to the open problem of showing existence of hadrons in the first place!).

      This is all well and widely known, but there is no culture as in mathematics of succinctly highlighting open problems such that one could refer to them easily.

      I have now created a section References – Phenomenology to eventually collect references that come at least close to making this nicely explicit. (Also checked with the PF community here)

      diff, v4, current

    • tried to bring the entry Lie group a bit into shape: added plenty of sections and cross links to other nLab material. But there is still much that deserves to be done.

    • I have changed the name to Haar Integral – if that’s ok – since the perspective I have added to the article leaves Haar measure as a consequence of Haar integral, and not the other way around.

      edeany@umich.edu

      diff, v10, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • a small entry on the quantum T- and S-gates, just for completeness.

      v1, current

    • Added link to mentioned book and possible link to mentioned paper

      Julius

      diff, v20, current

    • make lists of conferences part of the category: reference

      Valeria de Paiva

      diff, v5, current

    • The link for ’equivalent’ at the top redirected to natural isomorphism which (as I understand it) is the correct 1-categorical version of an equivalence of functors, but this initially lead me to believe that a functor was monadic iff it was naturally isomorphic to a forgetful functor from the Eilenberg-Moore category of a monad on its codomain, which would mean that the domain of the functor was literally the Eilenberg-Moore category of some adjunction since natural isomorphism is only defined for parallel functors.

      diff, v19, current

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

      v1, current

    • a bare minimum, for the moment just to record some references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • This article is weird. What is the difference between the object described by it and the article submodule? Appears to be a duplicate.

      diff, v4, current

    • Created page.

      For now Pol (the category) redirects here. Let me know if this is okay.

      v1, current

    • added the statement of the Fubini theorem for ends to a new section Properties.

      (I wish this page would eventually give a good introduction to ends. I remember the long time when I banged my head against Kelly’s book and just didn’t get it. Then suddenly it all became obvious. It’s some weird effect with this enriched category theory that some of it is obvious once you understand it, but looks deeply mystifying to the newcomer. Kelly’s book for instance is a magnificently elegant resource for everyone who already understands the material, but hardly serves as an exposition of the ideas involved. I am hoping that eventually the nLab entries on enriched category theory can fill this gap. Currently they do not really. But I don’t have time for it either.)

    • Several recent updates to literature at philosophy, the latest being

      • Mikhail Gromov, Ergostructures, Ergologic and the Universal Learning Problem: Chapters 1, 2., pdf; Structures, Learning and Ergosystems: Chapters 1-4, 6 (2011) pdf

      which is more into cognition and language problem, but still very relevant, and by a top mathematician. As these 2 are still manuscripts I put them under articles, though I should eventually classify those as books…

    • Created:

      Definition

      Given vector subspaces V 0V_0 and V 1V_1 of a vector space VV, we write V 0≺V 1V_0\prec V_1 if V 0/(V 0∩V 1)V_0/(V_0\cap V_1) is finite-dimensional. We write V 0∼V 1V_0\sim V_1 and say V 0V_0 and V 1V_1 are commensurable if V 0≺V 1V_0\prec V_1 and V 1≺V 0V_1\prec V_0.

      A Tate vector space is a complete Hausdorff topological vector space VV that admits a basis of neighborhoods of 0 whose elements are mutually commensurable vector subspaces of VV.

      Duality

      A vector subspace WW of a Tate vector space VV is bounded if for every open vector subspace U⊂VU\subset V we have W≺UW\prec U.

      The dual of a Tate vector space VV is Hom(V,C)Hom(V,\mathbf{C}) equipped with a topology generated by the basis of neighborhoods of 0 whose elements are orthogonal complements to bounded subspaces of VV.

      Properties

      Tate vector spaces form an pre-abelian category.

      References

      v1, current

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