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    • seeing Eric create diffeology I became annoyed by the poor state that the entry diffeological space was in. So I spent some minutes expanding and editing it. Still far from perfect, but a step in the right direction, I think.

      (One day I should add details on how the various sites in use are equivalent to using CartSp)

    • Characterized full faithfulness in terms of a pullback

      diff, v15, current

    • edited classifying topos and added three bits to it. They are each marked with a comment "check the following".

      This is in reaction to a discussion Mike and I are having with Richard Williamson by email.

    • I have started working on Diff: added a subsection with discussion of its properties as a site.

      Added statement and proof of the fact that

      • Sh(Diff)Sh(Diff) is a cohesive topos (direct consequence of the comparison lemma)

      • Sh (,1)(Diff)Sh_{(\infty,1)}(Diff) is a cohesive (infinity,1)-topos (easy with some lemmas from the literature, but not immediate (I think))

    • brief category:people-entry for hyperlinking references

      v1, current


      Suggests that Stone, Gelfand, … duality are special cases of the adjunction between CoPresheaves and Presheaves. A similar question is raised here.

      However, this paper

      seems to use another definition. Could someone please clarify?

    • In the section “In terms of truncations” I have added a few more cross links (both between the definitions in that section as well as to the respective items in HTT).

      diff, v55, current

    • Just noticed that when this page is shown in a Google search, the link from the Google page does not work. It seems that the “+” sign that used to be in the entry title gets interpreted as a whitespace.

      Therefore I am now changing the page name, replacing “+” by “and”. This should fix the problem, once Google picks up the change.

      diff, v11, current

    • discovered this old entry. Am renaming it to bijective on objects functor, for readability, making the previous “bo functor” a redirect

      diff, v11, current

    • a bare list of entry names, to be !include-ed into the “Related concepts”-sections of the relevant entries – for ease of cross-linking

      v1, current

    • started to add to internalization a list of links to examples. Probably we have much more.

    • As an outcome of recent discussion at Math Overflow here, Mike Shulman suggested some nLab pages where comparisons of different definitions of compactness are rigorously established. I have created one such page: compactness and stable closure. (The importance and significance of the stable closure condition should be brought out better.)

    • am starting some minimum here. Have been trying to read up on this topic. This will likely become huge towards beginning of next year

      v1, current

    • Added a reference

      • John Rognes, Galois extensions of structured ring spectra/Stably dualizable groups, Memoires of the American Mathematical Society, 192(898), 2008, partly available as (pdf)

      diff, v11, current