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    • 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

    • Added a reference to

      • Christian Maurer, Universes in Topoi , pp.285-296 in Lawvere, Maurer, Wraith (eds.), Model Theory and Topoi , LNM 445 Springer Heidelberg 1975.

      diff, v19, current

    • some minimum, just for completeness

      v1, current

    • Created a page for the homonymous cartesian theory.

      v1, current

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

      v1, current

    • Replace “infinity” with “∞”.

      Mark John Hopkins

      diff, v6, current

    • stub entry, for the moment just to record the reference

      v1, current

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

      v1, current

    • made explicit that for a normal subgroup NGN \subset G its “Weyl group” in the sense of W HG(N GH)/HW_H G \coloneqq (N_G H)/H coincides with the plain quotient group G/NG/N.

      diff, v8, current