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    • Created an entry for this.

      I’ve adopted the existing convention at nLab in the definition of Tw(C)Tw(C) (which is also the definition I prefer).

      Since the opposite convention is used a lot (e.g. by Lurie), I’ve decided it was worth giving it notation, the relation between the versions, and citing results in both forms. Since I didn’t have any better ideas, I’ve settled on Tw¯(C)\overline{Tw}(C).

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

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

      Anonymous

      v1, current

    • For completeness I have added pointer to

      though there should really be some accompanying discussion of how this form of the statement is related to the usual one in terms of presheaves.

      diff, v13, current

    • Created:

      Idea

      An alternative to complete topological vector spaces in the framework of condensed mathematics.

      Roughly, completeness is expressed as ability to integrate with respect to Radon measures.

      This doesn’t quite work as stated, and to make this rigorous one has to bring L^p-spaces for 0<p≤10\lt p\le 1 (i.e., the non-convex case) into the picture.

      Definition

      A condensed abelian group VV is pp-liquid (0<p≤10\lt p\le 1) if for every compact Hausdorff topological space SS and every morphism of condensed sets f:S→Vf\colon S\to V there is a unique morphism of condensed abelian groups M Unknown characterp(S)→VM_{<p}(S)\to V that extends ff along the inclusion S→M Unknown characterp(S)S\to M_{<p}(S).

      Here for a compact Hausdorff topological space SS and for any pp such that 0Unknown characterp≤10<p\le 1 we have

      M Unknown characterp(S)=⋃ qUnknown characterpM q(S),M_{<p}(S)=\bigcup_{q<p}M_q(S),

      where

      M p(S)=⋃ CUnknown character0M(S) ℓ p≤C,M_p(S)=\bigcup_{C>0}M(S)_{\ell^p\le C},

      where

      M(S) ℓ p≤C=lim iM(S i) ℓ p≤C,M(S)_{\ell^p\le C}=\lim_i M(S_i)_{\ell^p\le C},

      where S iS_i are finite sets such that

      S=lim iS iS = \lim_i S_i

      and

      M(F) ℓ p≤CM(F)_{\ell^p\le C}

      for a finite set FF denotes the subset of R F\mathbf{R}^F consisting of sequence with l^p-norm at most CC.

      References

      See condensed mathematics.

      v1, current

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

      Anonymous

      v1, current

    • the (infinity,1)-category of condensed infinity-groupoids has all finite (infinity,1)-limits, so it should have spectrum objects.

      Anonymous

      v1, current

    • polynomials are a concept from abstract algebra, and it is not true that all polynomials are continuous as (non-trivial) topological vector spaces over a field with a (non-trivial) metric space; polynomials over finite fields are one such counterexample: they are only continuous when equipped with the discrete or indiscrete topology and the finite field is equipped with the trivial metric.

      This article is about polynomial functions over the real numbers and epsilontic pointwise continuity of such functions.

      Anonymous

      diff, v5, current

    • hopefully the given definition makes sense and is equivalent to the definition found in Scholze’s “Lectures on analytic geometry”, somebody more knowledgeable at (∞,1)(\infty,1)-category theory could double check.

      Anonymous

      v1, current

    • these are real-valued rational functions and continuity here is pointwise continuity

      Anonymous

      diff, v2, current

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

    • finally found this textbook, am giving it it’s own category:reference-entry hereby, for ease of cross-linking

      have started to make a hyperlinked index for the chapters.

      v1, current

    • starting something (prodded by the comment here), but just a bare minimum for the moment

      v1, current

    • Created a stub. Will be expanded eventually.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • starting an entry, for the moment mainly in order to record the fact that “crossed homomorphisms” are equivalently homomorphic sections of the corresponding semidirect product group projection. This is obvious, but is there a reference that makes it explicit?

      v1, current

    • bare minimum, for the moment just so that one may link to it

      v1, current

    • Had a bit of clean up of entanglement, check the previous revision to see the section I deleted.

    • this is a bare list of references which used to be (and still is) at entanglement entropy. But since the same references are now also needed at long-range entanglement, I am putting them in a separate page here, to be !include-ed into both these entries

      v1, current

    • Only a stub at the moment, but I thought we needed to start a page on this. Looks like it’s going to become important.

      v1, current

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

      Anonymous

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category: people-entry for hyperlinking references

      v1, current

    • brief category: people-entry for hyperlinking references

      v1, current

    • brief category: people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

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

      Anonymous

      v1, current

    • Made explicit the notion of quantum dimension, and made that term redirect here (for the time being).

      diff, v5, current

    • added pointer to today’s

      • Matthew Headrick, Lectures on entanglement entropy in field theory and holography (arXiv:1907.08126)

      diff, v3, current

    • Spelled out the (equivalent) definition of locally small indexed category, and noted the equivalence of 2-categories explicitly.

      Eigil Rischel

      diff, v6, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • touching this ancient and abandoned entry in reaction to the discussion here:

      I think an entry with this title deserves to exist (even if its current content is unsatisfactory). To make this point, I am cross-linking it now with all of the following entries which all exist (even though all of them leave a lot of room for improvement):

      In this vein, I have removed the category: meta-tag from this entry.

      diff, v4, current

    • I am taking the liberty of creating a category: reference-entry in order to have a way to hyperlink references to our new research center here in NYUAD, which is slowly but surely entering into tangible existence.

      v1, current

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

      Anonymous

      v1, current

    • I added to field a mention of some other constructive variants of the definition, with a couple more references.

    • have added to codomain fibration a brief paragraph on the (∞,1)(\infty,1)-version here and that it’s a coCartesian fibration.

    • starting someting – not done yet but need to save

      v1, current

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

      Anonymous

      v1, current

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

      Anonymous

      v1, current

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

      Anonymous

      v1, current

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