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

      v1, 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

    • 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

    • 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

    • stub for confinement, but nothing much there yet. Just wanted to record the last references there somewhere.

    • 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 0V 1V_0\prec V_1 if V 0/(V 0V 1)V_0/(V_0\cap V_1) is finite-dimensional. We write V 0V 1V_0\sim V_1 and say V 0V_0 and V 1V_1 are commensurable if V 0V 1V_0\prec V_1 and V 1V 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 UVU\subset V we have WUW\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

    • disambiguation page for Ore condition

      watcher

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • renaming page to “Ore condition in a category” because there also exists the Ore condition in ring theory

      watcher

      diff, v6, current

    • I added some material to Peano arithmetic and Robinson arithmetic. At the latter, I replaced the word “fragment” (which sounds off to my ears – actually Wikipedia talks about thisterm a little) with “weakening”.

      Still some links to be inserted.

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

      Anonymous

      v1, current

    • Included the condition on sequential (co)limits that the indexing ordinal should be nonzero, which I presume to be the correct convention. (e.g. based on the description they are a special case of filtered colimits)

      diff, v8, current

    • starting disambiguation page for twisted arrow

      Anonymouse

      v1, current

    • starting page on the twisted arrow modality in simplicial type theory

      Anonymouse

      v1, current

    • 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

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

      v1, current

    • At coverage, I just made the following change: Where the sheaf condition previously read

      X(U) iIX(U i) i,jIX(U i× UU j), X(U) \to \prod_{i\in I} X(U_i) \rightrightarrows \prod_{i,j\in I} X(U_i\times_U U_j),

      it now uses the variable names “jj” and “kk” instead of “ii” and “jj”:

      X(U) iIX(U i) j,kIX(U j× UU k). X(U) \to \prod_{i\in I} X(U_i) \rightrightarrows \prod_{j,k\in I} X(U_j\times_U U_k).

      I’m announcing this almost trivial change because I’d like to invite objections, in which case I’d rollback that change and also would not go on to copy this change to related entries such as sheaf. There are two tiny reasons why I prefer the new variable names:

      • It’s more symmetric. The previous notation unjustly favored “ii”.
      • It’s slightly easier to infer the definition of the two maps. (I had a student who was briefly confused by the original notation.)
    • Added a lemma about fully faithful functors.

      Sorry for the mess, there does not seem to be a way to preview edits.

      diff, v3, current

    • starting stub article on synthetic (,1)(\infty,1)-category

      Anonymous

      v1, current

    • starting page on the op modality in simplicial type theory and synthetic (infinity, 1)-category theory

      Anonymouse

      v1, current

    • starting page on spatial type theory, which is modal dependent type theory with the sharp and flat modalities.

      Anonymous

      v1, current

    • The entry (infinity,1)-Kan extension is still a sad stub which you shouldn’t look at if you have better things to do. But I have now briefly added at least a few more specific pointers to HTT, in particular to the pointwise-ness issue. But just pointers, essentially no text for the moment. (If you feel energetic, be invited to turn the entry into something prettier!)

    • 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

    • brief category:people-entry for hyperlinking references

      v1, current

    • starting stub on simplicial type theory

      Anonymous

      v1, current

    • starting something, but my battery is dying and it remains a stub

      v1, current

    • In most recent works, quantale is defined more generally, as a semigroup in the monoidal category of suplattices.

      diff, v35, 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.

      v1, current

    • making this a stand-alone entry (“2-sphere” used to redirect to sphere, which however ended up being about nn-spheres in generality)

      but it is just a stub for the time being. Mainly I was looking to make a home for these references on ΩS 2\Omega S^2:

      in relation to braid groups:

      • Frederick R. Cohen, J. Wu: On Braid Groups, Free Groups, and the Loop Space of the 2-Sphere, in: Categorical Decomposition Techniques in Algebraic Topology, in Progress in Mathematics 215, Birkhäuser (2003) 93-105 [doi:10.1007/978-3-0348-7863-0_6]

      and regarded as a classifying space, ΩS 2BΩ 2S 2\Omega S^2 \,\simeq\, B \Omega^2 S^2 (for “l\mathbf{l}ine” bundles):

      v1, current

    • subdivided the Properties-section into subsections; added subsection for branched coverings of nn-spheres

      diff, v39, current