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    • created Lie bialgebra, but so far just a comment on their quantization.

    • This is intended to continue the issues discussed in the Lafforgue thread!

      I have added an idea section to Morita equivalence where I sketch what I perceive to be the overarching pattern stressing in particular the two completion processes involved. I worked with ’hyphens’ there but judging from a look in Street’s quantum group book the pattern can be spelled out exactly at a bicategorical level.

      I might occasionally add further material on the Morita theory for algebraic theories where especially the book by Adamek-Rosicky-Vitale (pdf-draft) contains a general 2-categorical theorem for algebraic theories.

      Another thing that always intrigued me is the connection with shape theory where there is a result from Betti that the endomorphism module involved in ring Morita theory occurs as the shape category of a ring morphism in the sense of Bourn-Cordier. Another thing worth mentioning on the page is that the Cauchy completion of a ring in the enriched sense is actually its cat of modules (this is in Borceux-Dejean) - this brings out the parallel between Morita for cats and rings.

    • added table of contents, headers, and added an overview page for how size issues are handled by using some notion of universe, and what those universes are in different foundations.

      Anonymous

      diff, v2, current

    • Adjusted the wording of the Idea-section for clarity and flow, and hyperlinked more of the technical terms.

      diff, v15, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • have added to Topos in the section on limits of toposes the description of the pullback of toposes by pushout of their sites of definition.

    • added this pointer:

      • Christian Blanchet, Marco De Renzi, Modular Categories and TQFTs Beyond Semisimplicity (arXiv:2011.12932)

      diff, v9, current

    • I added to excluded middle a discussion of the constructive proof of double-negated LEM and how it is a sort of “continuation-passing” transform.

    • I created a page for Riemannian metric based on a "blog post": http://deltaepsilons.wordpress.com/2009/10/27/riemannian-metrics-and-connections/ and a suggestion of Urs Schreiber.

    • This comment is invalid XHTML+MathML+SVG; displaying source. <div> <p>created <a href="https://ncatlab.org/nlab/show/nonabelian+group+cohomology">nonabelian group cohomology</a></p> <p>the secret title of this entry is "Schreier theory done right". (where "right" is right from the <a href="https://ncatlab.org/nlab/show/nPOV">nPOV</a>)</p> <p>this is the first part of the answer to</p> <blockquote> What is going on at <a href="https://ncatlab.org/nlab/show/nonabelian+Lie+algebra+cohomology">nonabelian Lie algebra cohomology</a>? </blockquote> <p>The second part of the answer is the statement:</p> <blockquote> The same. </blockquote> <p>;-)</p> <p>I'll expand on that eventually.</p> </div>
    • Switch from binary to unbiased definition, which excludes the empty space from being irreducible.

      diff, v6, current

    • Mike Stay kindly added the standard QM story to path integral.

      I changed the section titles a bit and added the reference to the Baer-Pfaeffle article on the QM path integral. Probably the best reference there is on this matter.

    • “Ass” is used for both the associative operad and the category of assemblies

      George Harrison

      v1, current

    • added to S-matrix a useful historical comment by Ron Maimon (see there for citation)

    • starting to collect references on string/M-theory compactifications on K3-compactifications (here). Am also touching related entries such as Moonshine etc.

      diff, v14, current

    • starting article on Feynman polytopes in the S-matrix program

      Theresa

      v1, current

    • Started a page on cosmohedra

      Theresa

      v1, current

    • Starting page on Tr(ϕ 3)\mathrm{Tr}(\phi^3)

      Anonymouse

      v1, current

    • Jim Stasheff pointed out a reference that discusses categorifications of associahedra. I added the ref to associahedron

    • Created a stub for this concept.

      v1, current

    • starting something, but not much here yet.

      Eventually I’d like to make a linked cube diagram of flavors of Hall effects (±\pmquantum, ±\pmanomalous, ±\pmfractional). Something like this was attempted in Figure 1 of

      • Nicolás Morales-Durán, Jingtian Shi, A. H. MacDonald: Fractionalized electrons in moiré materials, Nature Reviews Physics 6 (2024) 349–351 [doi:10.1038/s42254-024-00718-z]

      but maybe we can improve on that…

      v1, current

    • I have considerably expanded the entry sigma-model and will probably continue to do so in small steps in the nearer future (with interruptions). This goes in parallel with a discussion we are having on the nnCafé here.

    • In light of people such as Taichi Uemura using assemblies in areas unrelated to realizability, I’ve decided to split off the text on assemblies and its category from realizability topos to its own article.

      George Harrison

      v1, current

    • Corrected a hyperlink. Removed the publication year from the page title.

      diff, v2, current

    • am finally giving this an entry of its own

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:peopleentry for hyperlinking references

      v1, current

    • stub for 2-topos (mostly so that the links we have to it do point somewhere at least a little bit useful)

    • brief category:people-entry for hyperlinking references

      v1, current

    • starting page on Christophe Cordero for the sake of a reference at associative operad

      Abe

      v1, current

    • Todd,

      when you see this here and have a minute, would you mind having a look at monoidal category to see if you can remove the query-box discussion there and maybe replace it by some crisp statement?

      Thanks!

    • added more references to 2-spectral triple (as far as I can see Jürg Fröhlich with his students was the first to try to formalize this to some extent)

    • a bare list of references (for articles considering “unstable” or “fragile” classification of topological phases of matter, not in K-theory but by the non-abelian cohomology classified by finite-dimensional Grassmannians or flag manifolds)

      to be !include-ed into the list of references at relevant entries, for ease of synchronizing

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • added the remark that

      P 1Gr 1( 2)U(2)/(U(1)×U(1)) \mathbb{C}P^1 \,\simeq\, Gr_1(\mathbb{C}^2) \,\simeq\, \mathrm{U}(2)/\big(\mathrm{U}(1) \times \mathrm{U}(1)\big)

      diff, v14, current

    • I decided it would be a good idea to split off realizability topos into a separate entry (it had been tucked away under partial combinatory algebra). I’ve only just begun, mainly to get down the connection with COSHEP. A good (free, online) reference is Menni’s thesis.

    • Added that there’s a dual concept of weak colimits.

      diff, v12, 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

    • starting something on “anomalous velocity” (of electron motion in the space of Bloch momenta, caused by non-vanishing Berry curvature)

      v1, current