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    • 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 V0 and V1 of a vector space V, we write V0V1 if V0/(V0V1) is finite-dimensional. We write V0V1 and say V0 and V1 are commensurable if V0V1 and V1V0.

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

      Duality

      A vector subspace W of a Tate vector space V is bounded if for every open vector subspace UV we have WU.

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

      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) (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).

      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(Ui)i,jIX(Ui×UUj),

      it now uses the variable names “j” and “k” instead of “i” and “j”:

      X(U)iIX(Ui)j,kIX(Uj×UUk).

      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 “i”.
      • 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)-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

      • Emily Riehl, Dominic Verity, Section 6 of: Fibrations and Yoneda’s lemma in an -cosmos, Journal of Pure and Applied Algebra Volume 221, Issue 3, March 2017, Pages 499-564 (arXiv:1506.05500, doi:10.1016/j.jpaa.2016.07.003)

      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 n-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 ΩS2:

      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, ΩS2BΩ2S2 (for “line” bundles):

      v1, current

    • Added pointers to the Hanany-Witten construction and cross-linked with new section at NS5-brane on D-branes ending on NS5-branes.

      diff, v6, 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

    • brief category:peole-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • added pointer to these two recent references, identifying further L-algebra structure in Feynman amplitudes/S-matrices of perturbative quantum field theory:

      • Markus B. Fröb, Anomalies in time-ordered products and applications to the BV-BRST formulation of quantum gauge theories (arXiv:1803.10235)

      • Alex Arvanitakis, The L-algebra of the S-matrix (arXiv:1903.05643)

      diff, v11, current

    • have hyperlinked the keywords under “Contents”, as far as nLab entries exist for them

      diff, v4, current