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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

• 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.

• made this a disambiguation page (previously it was the name of the entry now called SmoothManifolds)

• 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

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

• $Sh_{(\infty,1)}(Diff)$ 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

• there is a blog entry to go with this here

• http://ncatlab.org/nlab/show/Isbell+duality

Suggests that Stone, Gelfand, … duality are special cases of the adjunction between CoPresheaves and Presheaves. A similar question is raised here. http://mathoverflow.net/questions/84641/theme-of-isbell-duality

However, this paper http://www.emis.ams.org/journals/TAC/volumes/20/15/20-15.pdf

seems to use another definition. Could someone please clarify?

• The page on inductive-inductive types refers to dialgebras without specifying them. Having a short page as some sort of reference is helpful.

• Added some intuition for coskeleta

• created page, more to come

• 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).

• Created.

• Mention dual Yoneda embedding.

• 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.

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

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

• 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