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- Discussion Type
- discussion topicQuestion on Grothendieck fibrations.
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by Mike Shulman
- Last Active Dec 30th 2009

Sridhar Ramesh has one at Grothendieck fibration.

- Discussion Type
- discussion topiccellular set
- Category Latest Changes
- Started by zskoda
- Comments 5
- Last comment by TobyBartels
- Last Active Dec 30th 2009

cellular set, mainly references for now

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

- Discussion Type
- discussion topicGrothendieck fibration+topological K-theory
- Category Latest Changes
- Started by Guest
- Comments 6
- Last comment by domenico_fiorenza
- Last Active Dec 28th 2009

- 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

- Discussion Type
- discussion topiccodomain stacks
- Category Latest Changes
- Started by Mike Shulman
- Comments 2
- Last comment by Urs
- Last Active Dec 28th 2009

Added comments to regular category, exact category, coherent category, and pretopos about under precisely what conditions the codomain fibration is a stack for the relevant Grothendieck topology. Also added some thoughts about "pre-lextensive categories" to extensive category.

- Discussion Type
- discussion topicAlgebraic categories
- Category Latest Changes
- Started by TobyBartels
- Comments 14
- Last comment by Mike Shulman
- Last Active Dec 24th 2009

I started algebraic category, with a note also at monadic adjunction.

- Discussion Type
- discussion topicoo-limits - contents
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by TobyBartels
- Last Active Dec 24th 2009

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)

- Discussion Type
- discussion topicbutterfly
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Dec 23rd 2009

started expanding butterfly

also butterfly diagrams at crossed profunctor

- Discussion Type
- discussion topicdeRham theorem for oo-Lie groupoids
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 22nd 2009

filled a gap in deRham theorem for oo-Lie groupoids on my personal web.

But I need to sleep over this...

- Discussion Type
- discussion topiccontractible objects in a lined topos
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Dec 22nd 2009

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 is such that all representable objects are contractible with respect to the line object , then the path oo-groupoid functor

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).

- Discussion Type
- discussion topicshape fibration
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Dec 22nd 2009

An incomplete introduction to shape fibration and a related bio entry Sibe Mardesic.

- Discussion Type
- discussion topicBeckâ€“Chevalley
- Category Latest Changes
- Started by TobyBartels
- Comments 7
- Last comment by zskoda
- Last Active Dec 22nd 2009

Somebody wrote quite the stub at Beck-Chevalley_Condition; I fixed the name but didn't mess with it otherwise. It seems to have appeared (properly named) on Mike's web too, all by the AnonymousCoward.

- Discussion Type
- discussion topicAtiyah Lie groupoid
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Dec 21st 2009

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:

split off Atiyah Lie algebroid from Atiyah Lie groupoid

created a section Relation to differential nonabelian cohomology at Atiyah Lie groupoid that states a claim on how the Atiyah Lie groupoid fits into the story of nonabelian groupoid cohomology -- I wanted to type the proof, too, but ran out of time. Either someone takes it as an exercise and provides the proof, or I'll do so myself later today (or tomorrow)

created a stub for nonabelian groupoid cohomology. There exists a nice reference on "groupoid Schreier theory" that should go there, but I don't have time for that now

created inner automorphism 2-group to provide some background information needed in the statement of the above claim

- Discussion Type
- discussion topicJohn Baez's Towards Higher Categories
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Urs
- Last Active Dec 21st 2009

I worked on polishing

on John Baez's web. I

added hyperlinks to all the names appearing

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.

- Discussion Type
- discussion topicspace and quantity
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 21st 2009

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)

- Discussion Type
- discussion topicbar construction
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 18th 2009

homeopathic definition at bar construction

- Discussion Type
- discussion topic(n,r)-fibrations
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 18th 2009

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.

- Discussion Type
- discussion topicnonabelian group cohomology
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by zskoda
- Last Active Dec 18th 2009

`<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>`

- Discussion Type
- discussion topicelementary treatment of Hilbert spaces
- Category Latest Changes
- Started by Andrew Stacey
- Comments 8
- Last comment by Andrew Stacey
- Last Active Dec 18th 2009

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.

- Discussion Type
- discussion topicFixed broken links
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Dec 17th 2009

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

- Discussion Type
- discussion topicNew stubs
- Category Latest Changes
- Started by TobyBartels
- Comments 4
- Last comment by TobyBartels
- Last Active Dec 16th 2009

Just look at the list of all wanted pages, here are a few stubby articles: 1-topos, 2-Hilbert space, Alexandroff compactification, Banach manifold. (Yes, I went alphabetically.)

- Discussion Type
- discussion topicNo more orphaned pages!
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Dec 16th 2009

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.

- Discussion Type
- discussion topicoo-Lie theory - contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 16th 2009

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".

So I created a floating table of contents

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.

- Discussion Type
- discussion topicstrict 2-group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 16th 2009

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).

- Discussion Type
- discussion topicRiemann surfaces and Myers-Steenrod theorem
- Category Latest Changes
- Started by amathew
- Comments 3
- Last comment by amathew
- Last Active Dec 15th 2009

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

- Discussion Type
- discussion topicstring Lie 2-algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 15th 2009

added the detailed definition to string Lie 2-algebra

- Discussion Type
- discussion topicNew page: [[classical mathematics]]
- Category Latest Changes
- Started by TobyBartels
- Comments 27
- Last comment by Urs
- Last Active Dec 15th 2009

I started classical mathematics to link to from internal logic.

- Discussion Type
- discussion topicframed bicategory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by TobyBartels
- Last Active Dec 13th 2009

created quick stub for framed bicategory

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

- Discussion Type
- discussion topicEdit conflict at [[model structure on dendroidal sets]]
- Category Latest Changes
- Started by TobyBartels
- Comments 4
- Last comment by TobyBartels
- Last Active Dec 11th 2009

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.

- Discussion Type
- discussion topic(oo,1)-operads
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Dec 11th 2009

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

- Discussion Type
- discussion topicObjections by Maarten
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by Urs
- Last Active Dec 10th 2009

Or possibly not by Maarten. Anyway, there is some discussion at superdifferential form and Weil algebra that people into that sort of thing should look at.