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    • I was about to create a new entry “characteristic differential form” when I discrovered this old entry.

      Have added more redirects to it and more cross-links with Chern-Weil homomorphism.

      diff, v8, current

    • starting some minimum (this is for Cartan’s map in equivariant de Rham cohomology, maybe the entry deserves an expanded title for disambiguation)

      v1, current

    • I’m interested in editing Mac Lane’s proof of the coherence theorem for monoidal categories, as I recently went through all the gory details myself and wrote it up. I was wondering if anybody has any thoughts on what should be left alone with regard to any future changes. Many people clearly put in a lot of work into the page, but it looks like people got busy and it hasn’t been updated in a while.

      I think the first few paragraphs are fine, but I think the rest is a bit wordy, it could be more formal, and notation could be changed (very slightly) to be less clunky. I specifically want to make the current document more formal (e.g., saying “Definition: blah blah”), include some nice diagrams, change the notation (e.g., to avoid using double primes, to avoid denoting a monoidal category as B since I think the letter M pedagogically makes more sense), and complete the incomplete entries at the bottom. I’m not really sure if anyone would be against such changes, hence my inquiry.

    • a table to collect the various cases of transverse geometries to KK-monopoles, to be !include-ded into the relevant entries

      v1, current

    • this table used to be hidden at supersymmetry, but it really ought to cross-link its entries. Therefore here its stand-alone version, for !inclusion

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Simply the definition, as found in “Combinatorics of coxeter groups” by Bjorner and Brenti.

      Anonymous

      v1, current

    • added pointer to

      • Paul Balmer, The spectrum of prime ideals in tensor triangulated categories. J. Reine Angew. Math., 588:149–168, 2005 (arXiv:math/0409360)

      • Paul Balmer, Spectra, spectra, spectra—tensor triangular spectra versus Zariski spectra of endomorphism rings, Algebr. Geom. Topol., 10(3):1521–1563, 2010 (pdf)

      (which have been listed at Paul Balmer all along, but were missing here, strangely)

      and to the recent:

      diff, v9, current

    • some minimum, for completeness of the list at D4

      v1, current

    • This page had, besides its minimum content, somewhat weird formatting overhead. I have deleted that now, including the multiple category:-declarations

      diff, v3, current

    • Added a page about the category FinRel of finite sets and relations, and some of its properties.

      v1, current

    • Added the analogous sheaf condition in terms of covering families

      diff, v20, current

    • a category:reference-page to ease cross-linking

      v1, current

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

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • apparently this was a typo for and duplicate of Augusto Sagnotti – am clearing the entry (a stub anyway), adding redirect to the proper entry

      diff, v2, current

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

      v1, current

    • giving this its own little entry, for ease of hyperlinking

      v1, current

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

      v1, current

    • I have typed into infinitesimal interval object a detailed description of the simplicial object inuced on a microlinear space from the infinitesimal interval in immediate analogy to the construction of the finite path simplicial object induced from an interval object (as discussed there).

      I also give the inclusion of the infinitesimal simplicial object into the finite one.

      All the proofs here are straightforward checking, which I think I have done rather carefully on paper, but not typed up. What I would appreciate, though, is if somebody gave me a sanity check on the definition of the infinitesimal simplicial object (which is typed in detail).

      In the very last section, which is the one that is still just a sketch, I am hoping to describe an isomorphism from my simplicial infinitesimal object to that considered by Anders Kock, which is currently described at infinitesimal singular simplicial complex in the case that the space X satisfies Kock's assumptions (it must be a "formal manifold").

      The construction I discuss at infinitesimal interval object is supposed to generalize Kock's construction to all microlinear spaces and motivated by having that canonical obvious inclusion into the finite version at interval object.

      The isomorphism should be evident: my construction evidently yields in degree k k-tuples of pairwise first oder neighbours if the space X admits that notion. But I want to sleep over this statement one more night...

    • added this second-order-quote:

      Chen Ning Yang writes in C. N. Yang, Selected papers, 1945-1980, with commentary, W. H. Freeman and Company, San Francisco, 1983, on p. 567:

      In 1975, impressed with the fact that gauge fields are connections on fiber bundles, I drove to the house of S. S. Chern in El Cerrito, near Berkeley… I said I found it amazing that gauge theory are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added: “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.”

      diff, v6, current

    • added these two quotes:

      Yang wrote in C. N. Yang, Selected papers, 1945-1980, with commentary, W. H. Freeman and Company, San Francisco, 1983, on p. 567:

      In 1975, impressed with the fact that gauge fields are connections on fiber bundles, I drove to the house of S. S. Chern in El Cerrito, near Berkeley… I said I found it amazing that gauge theory are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added: “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.

      Yang expanded on this passage in an interview recorded as: C. N. Yang and contemporary mathematics, chapter in: Robin Wilson, Jeremy Gray (eds.), Mathematical Conversations: Selections from The Mathematical Intelligencer, Springer 2001, on p. 72 (GoogleBooks):

      But it was not just joy. There was something more, something deeper: After all, what could be more mysterious, what could be more awe-inspiring, than to find that the structure of the physical world is intimately tied to the deep mathematical concepts, concepts which were developed out of considerations rooted only in logic and the beauty of form?

      diff, v3, current

    • starting something. Not done yet, but need to save

      v1, current

    • I split off inhabited object from inhabited set.

      (moved Mike's and Toby's old discussion query box to the new entry, too)

      I added an Examples section with a remark about this issue in the context of Models for Smooth Infinitesimal Analysis, that I happen to be looking into.

      personally, I feel I need more examples still at internal logic to follow this in its full scope. I guess I should read the Elephant one day, finally.

      In the book Moerdijk-Reyes say in a somewhat pedestrian way that existential quantifiers in the internal logic of a sheaf topos are to be evaluated on covers, hence asking internally if a sheaf F has a (internally global) element means asking if for U \to * any cover of the point, there is a morphism U \to F.

      That's fine with me and I follow this in as far as the purpose of their book is concerned, but I need to get a better idea of how the logical quantifiers are formulate in internal logic in full generality.

    • Adding MetaPRL, RedPRL, and proto CLF as “descendants” of Nuprl.

      diff, v9, current

    • Page created. Feel free to add to or reorganize the content!

      v1, current

    • New page in order to drop some references.

      v1, current

    • Page created for now. More content to be added soon.

      v1, current

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