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• added to negative thinking an explicit list of related entries and the floating higher cat theory toc

I think this is important enough to show the reader as much of the grand picture as possible

• I figured that we could stand to have an article on TAC, so I started one.

The category of commutative von Neumann algebras is contravariantly equivalent to the category of localizable measurable spaces.

to measurable space, but see we don't have anything on localizability.

I also mentioned the theorem at von Neumann algebra. But what should one then say that a general von Neumann algebra is a noncommutative localizable measurable space? Normally one says noncommutative measure space.
• I may have overlapped an edit with you at initial algebra. ( It's no longer locked, but you didn't change it again, so maybe it timed out.)

• Over on MO Denis-Charles Cisinki kindly replied to some issues that I am recently working on here. See this.

• It's not technically part of the main nLab (yet), but I asked a question at

Cograph (ericforgy)

• Couple of points (pun not intended) at ionad. Also remark about categorified subobject classifiers

David Roberts
• I rearranged higher category theory - contents. It seemed wrong to have everything as a special case of $n$-categories/$(n,r)$-categories except for $\infty$-categories/$\omega$-categories. But it seemed right to list the latter up front, as the all-subsuming concept. So I basically reversed the order. (I also added a few entries.)

• Added to initial algebra the proof of Lambek's theorem, that the algebra structure of an initial algebra is an isomorphism. Also added to natural numbers object Freyd's finite colimit characterization in a topos, with a partial proof of same.
• I created [[Levi-Civita connection]].

• Created diagrammatic order. I attempted to strike a neutral tone in describing the dispute, but if you think I failed, please help.

• I've notices that the links at Klein 2-geometry to the earlier parts are broken (something to do with the pages at Geocities). I recall hearing that someone made some more permanent copies. Is this true and if so, where are they?

I said some embarrassingly naive things there, but one must preserve what progress was made.

-David Roberts
• created cochains on simplicial sets

I reference there a very useful but unpublished note by Peter May that he sent me by email after he got over his astonishment that I didn't know that the Eilenberg-Zilber E_oo operad acts on cochains on a simplicial set.

It would be great if I were allowed to upload this note to the nLab and link it at that entry. I'll see if I ask by email, but maybe Mike can mention it over lunch? I feel like Peter May feels already pestered enough by my ignorance.

• I expanded categorification a little.

I had intended to point to it from a MathOverflow question, but now I feel the entry is still too underdeveloped. Hopefully we'll eventually find the time and energy to enter the big examples that drive the interest in categorification.

• I started a page on braided monoidal 2-category. Not that I have anything interesting to say on the subject, but I would like to know how to get them as module 2-categories over a monoidal category.

• created [[thin homotopy]] to service [[bicategory]], at which I added the necessary qualifier ‘Hausdorff’ to the existence of the quotient of Pi_2 by thin homotopies. There is only a passing mention of the smooth version as I only needed the topological case.

-David Roberts

• At cartesian morphism a query/request for an anafunctor treatment of what is essentially the pseudofunctor associated to a fibration

David Roberts