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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• Partially spurred on by an MO question, I have started an entry on simple homotopy theory. I am also intrigued as to whether there is a constructive simple homotopy theory that may apply in homotopy type theory, but know so little (as yet) about that subject that this may be far fetched.

• Steve (Lack) has put a comment box on AT category. I have not been following that entry so am not able to reply to his point.

• I filled in content at n-truncated object of an (infinity,1)-category.

to go with my discussion with David Roberts. I had planned to go further and also write the entry on Postnikov twoers, but got distracted all day.

Apart from that I just added this link to Higher Topos Theory and did some editing there, added a table of contents, expanded the floating toc.

• I started editing the page on reflexive Banach spaces - in particular I corrected the definition and stuck in a mention of "James space". A link or reference is needed but I am currently a bit too frazzled/stressed to do further editing today.

• I have expanded at DHR category the Idea-section and added more hyperlinks.

• Joel Hamkins and Andy Putman made some comments about the nLab on MathOverflow, beneath an answer by Andrew.

It’s interesting to know what people’s perceptions are, even if they’re wrong. (And I would think that Andy P’s perception is wrong.) I don’t know what Andrew S has in mind when he says that Joel’s point is extremely easy to answer.

• Following a discussion on the algebraic topology list, I’ve written a proof of the contractibility of the space of embeddings of a smooth manifold in a reasonably arbitrary locally convex topological vector space. The details are on embedding of smooth manifolds and it also led to me creating shift space (I checked on MO to see if there was an existing name for this, and Bill Johnson said he hadn’t heard of it).

• added the recent Barwick/Schommer-Pries preprint to (infinity,n)Cat, together with a few more brief remarks.

• I have been working on the entry twisted bundle.

Apart from more literature, etc. I have started typing something like a first-principles discussion: first a general abstract definition from twisted cohomology in any cohesive $\infty$-topos, then unwinding this in special cases to obtain the traditional cocycle formulas found in the literature.

Needs more polishing here and there, but I have to pause now.

• created Lie bialgebra, but so far just a comment on their quantization.

• I noticed that we are lacking C-infinity algebra, so I very briefly created a very stubby stub (no time right now…)

• Added a new Properties section to connected object. Including a theorem which is a bit of a hack (where I leave it to others to decide if ’hack’ should be interpreted positively or negatively!).

• while polishing up type theory - contents I felt the need for entries called syntax and semantics. I have created these just so that the links to them are not grey, but I put in only something minimalistic . I could add some general blah-blah, but I’d rather hope some actual expert feels inspired to start with some decent paragraphs.

• Added to pasting diagram a reference to the bicategorical pasting theorem given by Verity in his thesis.

• In the Definition-section at reflective factorization system I found the “$\Psi$” and “$\Phi$” used in the text oppositely to how they appear in the displayed diagram. I think I have fixed this.