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

• cellular set, mainly references for now

BTW, Does anybody have a file or scan of Joyal's original 1997 article ?

• At Grothendieck fibration I wonder if we can make the definition less evil than the non-evil version there, with applications to Dold fibrations. Also the insertion of a necessary adjective at topological K-theory.

-David Roberts
• created infinity-limits - contents and added it as a toc to relevant entries

(maybe I shoulod have titled the page differently, but it doesn't matter much for a toc)

• created a section Contractible objects at lined topos.

This introduces and discusses a bit a notion of objects being contractible with respect to a specified line object (maybe the section deserves to be at interval object instead, not sure).

This notion is something I made up, so review critically. I am open for suggestions of different terminology. The concept itself, simple as it is (though not entirely trivial), I need for the discussion of path oo-groupoids of oo-stacks on my personal web:

if a lined Grothendieck topos $(\mathcal{T} = Sh(C),R)$ is such that all representable objects are contractible with respect to the line object $R$, then the path oo-groupoid functor

$\Pi : SSh(C) \to SSh(C)$

on simplicial sheaves, which a priori is only a Qulillen functor of oo-prestacks, enhances to a Quillen functor of oo-stacks (i.e. respects the local weak equivalences).

• I intend to considerbly expand the story at Atiyah Lie groupoid. But this afternoon I didn't get as far as I intended to, and now I have to quit and visit my parents. So this is to be continued. But so far I did this:

• I worked on polishing

Towards Higher Categories

on John Baez's web. I

• turned the remaining "infininty"s to "oo"s

I was almost done when the Lab broke down, though, it seems. Currently the server does not respond.

• Added to the Idea section at space and quantity a short paragraph with pointers to the (oo,1)-categorical realizations. (Parallel to the blog discussion here)

• no, I didn't create an entry with that title.

but I added to n-fibration a brief link, though, to the concept that is currently described at Cartesian fibration, which models Grothendieck fibrations of (oo,1)-categories.

This here is mainly to remind me that there is need to polish and reorganize the nLab entries on higher fibrations into something more coherent.

• This comment is invalid XHTML+MathML+SVG; displaying source. <div> <p>created <a href="http://ncatlab.org/nlab/show/nonabelian+group+cohomology">nonabelian group cohomology</a></p> <p>the secret title of this entry is "Schreier theory done right". (where "right" is right from the <a href="http://ncatlab.org/nlab/show/nPOV">nPOV</a>)</p> <p>this is the first part of the answer to</p> <blockquote> What is going on at <a href="http://ncatlab.org/nlab/show/nonabelian+Lie+algebra+cohomology">nonabelian Lie algebra cohomology</a>? </blockquote> <p>The second part of the answer is the statement:</p> <blockquote> The same. </blockquote> <p>;-)</p> <p>I'll expand on that eventually.</p> </div>
• I've started a page an elementary treatment of Hilbert spaces. The intention is to see how much of (simple) Hilbert space theory can be done without using the phrases "As a Hilbert space is a normed vector space ..." or "As a Hilbert space is a metric space ...".

I haven't gotten very far yet, as can be seen! Also, it's not intended to be Deep Mathematics (there's a mild centipedal justification on the page) but just playing with some ideas and trying to see what a Hilbert space really is.

• I fixed a bunch of broken links on the lab just now. In case anybody is wondering what all of those edits were.

• I have just made links to all of the contentful orphaned paged on the main nLab web. However, they may still be walled gardens; Instiki doesn't find those automatically.

In general, when you create a new page, it's a good idea to create a link to it from some existing page on a more general topic. (The links that I just made may not have been the best!) That way, it's more likely that people will actually find their way to your new page.

• I wanted to start expanding on the big story at nonabelian Lie algebra cohomology, but then found myself wanting to polish first a bit further the background material.

I came to think that it is about time to collect our stuff on "oo-Lie theory".

and added it to most of the relevant entries.

This toc is based on the one on my personal web here -- but much larger now -- and still contains some links to my web, where I am trying to develop the full story. If anyone feels ill-at-ease with these links to my personal web, let me know.

• considerably expanded the entry strict 2-group.

• Apart from adding an introductory discussion, and expanding the list of examples, in particular by adding that of automorphism 2-groups ...

• ... I in particular give the detailed translation prescription for how to encode a 2-group by a crossed module at In terms of crossed modules

This is to eventually serve as a supplement to the discussion at nonabelian group cohomology. So I spent some energy on disentangling the four different (though isomorphic) ways a crossed module gives rise to a 2-group (following my article with David Roberts).

• I created [[Riemann surface]] and [[Myers-Steenrod theorem]].

• created quick stub for framed bicategory

but my machine's battery will die any second now...

• It looked to me like Urs hit Ctrl-V instead of Ctrl-C there, so I rolled back, but now Urs is editing again, so probably he's just doing something that I interrupted. Since I can't leave a note there now, I'll leave one here: I won't interfere again, Urs.

• added to (infinity,1)-operad the definition/proposition of the model structure for the category of (oo,1)-categories of operations here