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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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- Discussion Type
- discussion topicConvergence
- Category Latest Changes
- Started by TobyBartels
- Comments 6
- Last comment by TobyBartels
- Last Active Jun 21st 2013

Urs created limit of a sequence on this topic.

- Discussion Type
- discussion topicsuper line 2-bundle
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 20th 2013

I have finally split off

*super line 2-bundle*to a stand-alone entry (it used to be a subsection at*line 2-bundle*).

- Discussion Type
- discussion topichereditarily finite set
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jun 20th 2013

I discovered via MO that we have an entry

*hereditarily finite set*, which was a bit lonesome. So I have now tried to cross-link it a bit with related entries.In particular at

*finite object*in “Related entries” I started a list with related entries – probably incomplete, please expand. In the course of this I created als a brief entry*finite (infinity,1)-category*by splitting off a paragraph form finite (infinity,1)-limit.

- Discussion Type
- discussion topicArity
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by Mike Shulman
- Last Active Jun 19th 2013

I saw that one of the classical arity classes didn't have a name, so I named it ‘subunary’.

- Discussion Type
- discussion topicgraded field, infinity-field
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jun 18th 2013

last Friday, when the nForum was down, I had created very brief entries

and

- Discussion Type
- discussion topicQuery at Ronnie Brown
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Jun 18th 2013

I just deleted the query

Did you do these edits attributed to ’Ronald null Brown’? —Toby

at Ronnie Brown.

- Discussion Type
- discussion topicSemicontinuity
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Jun 18th 2013

A bit of classical stuff at semicontinuous map.

- Discussion Type
- discussion topicB-model
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by zskoda
- Last Active Jun 17th 2013

started a stub for the B-model

- Discussion Type
- discussion topicintegral Morava K-theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 17th 2013

stub for

*integral Morava K-theory*

- Discussion Type
- discussion topicDiaconescu-Moore-Witten anomaly
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 17th 2013

created

*Diaconescu-Moore-Witten anomaly*, so far just with a bunch of (briefly commented) references

- Discussion Type
- discussion topicheight of a formal group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 17th 2013

put the bare minimum definition into

*height of a formal group*

- Discussion Type
- discussion topicKan-Thurston Theorem
- Category Latest Changes
- Started by MatanP
- Comments 5
- Last comment by Charles Rezk
- Last Active Jun 15th 2013

- added an entry for the Kan Thurston Theorem.

http://ncatlab.org/nlab/show/Kan-Thurston+Theorem

- Discussion Type
- discussion topicFirewall problem
- Category Latest Changes
- Started by Noon
- Comments 17
- Last comment by TobyBartels
- Last Active Jun 15th 2013

A few grad students and I are starting a reading group on the Firewall problem and related aspects, so I’ve created a page in the nLab with a bunch of relevant papers:

(not yet a complete list.)

The goal will be to develop the page into a introduction to the problem, and the resolutions proposed, etc.

- Discussion Type
- discussion topicnoncommutative motives - table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 13th 2013

I have created a table

and included it into the relevant entries.

It looks like this:

geometric context universal additive bivariant (preserves split exact sequences ) universal localizing bivariant (preserves all exact sequences) universal additive invariant universal localizing invariant noncommutative algebraic geometry noncommutative motives $Mot_{add}$ noncommutative motives $Mot_{loc}$ algebraic K-theory non-connective algebraic K-theory noncommutative topology KK-theory E-theory operator K-theory … I am not sure what should go in the bottom right corner.

- Discussion Type
- discussion topicnon-connective algebraic K-theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 13th 2013

stub for

*non-connective algebraic K-theory*

- Discussion Type
- discussion topicmotivic cohomology - contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 12th 2013

you all knew it was about to happen, and now it did: I have created a table-of-contents page for inclusion as “floating TOC” in the relevant entries:

- Discussion Type
- discussion topiclimit in a quasi-category
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Jun 12th 2013

added to limit in a quasi-category (in the Properties-section) more details on how the definition in terms of over over-categories is equivalent to the one in terms of homs. But still not done.

- Discussion Type
- discussion topicorthogonal factorization system in an (oo,1)-category
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jun 12th 2013

started orthogonal factorization system in an (∞,1)-category in order to record the n-connected/n-truncated system for $(-2) \leq n \leq \infty$.

Notice that for this application our “connected”-convention is really nicer than the “connective” convention.

- Discussion Type
- discussion topicmotivic Donaldson-Thomas invariant
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 12th 2013

added Soibelman’s lectures notes to the list of references at

*motivic Donaldson-Thomas invariant*

- Discussion Type
- discussion topicmotivic function
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 12th 2013

quick note on

*motivic function*

- Discussion Type
- discussion topicexp & log
- Category Latest Changes
- Started by TobyBartels
- Comments 8
- Last comment by TobyBartels
- Last Active Jun 12th 2013

New articles: exponential map, logarithm.

- Discussion Type
- discussion topicrelative (infinity,1)-colimit
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 11th 2013

added the definition of

*relative (infinity,1)-limit*, because I need to point to it from elsewhere.(Somehow the cache bug, or a new version of it kicked in, and there is now also

*relative (∞,1)-limit*, which I won’t try to fight with just right now…)

- Discussion Type
- discussion topicSome new entries relating to functional analysis
- Category Latest Changes
- Started by Andrew Stacey
- Comments 16
- Last comment by TobyBartels
- Last Active Jun 9th 2013

- convergence vector space
- bounded set this used to redirect to bornalogical space
- continuous multilinear operator
- Fréchet derivative
- precompact set

(I’m currently reading through Keller’s book

*Differential Calculus in Locally Convex Spaces*.)

- Discussion Type
- discussion topicBaum-Douglas geometric cycle
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 8th 2013

- Discussion Type
- discussion topicbivariant algebraic K-theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 8th 2013

*bivariant algebraic K-theory*– for the moment just for recording some references

- Discussion Type
- discussion topicPartial differentiation.
- Category Latest Changes
- Started by TobyBartels
- Comments 11
- Last comment by TobyBartels
- Last Active Jun 7th 2013

I wrote partial differentiation. Also some remarks at chain rule.

- Discussion Type
- discussion topicSlideshow sandbox
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by Tim_Porter
- Last Active Jun 7th 2013

Someone (probably in Gottingen) created a slideshow page. I renamed it Slideshow sandbox and removed its contents which were

www.math.columbia.edu/~woit/notes16.pdf

That was the old name as well.

- Discussion Type
- discussion topiccosmic Galois group
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Jun 7th 2013

stub for

*cosmic Galois group*

- Discussion Type
- discussion topicnumerical motive
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 6th 2013

briefly started

*numerical motive*.

- Discussion Type
- discussion topicEuclid
- Category Latest Changes
- Started by TobyBartels
- Comments 18
- Last comment by Todd_Trimble
- Last Active Jun 5th 2013

- Discussion Type
- discussion topic[submersion]
- Category Latest Changes
- Started by DavidRoberts
- Comments 20
- Last comment by TobyBartels
- Last Active Jun 5th 2013

Urs created submersion and I added a little more. Still a bit stubby, though.

- Discussion Type
- discussion topicS-construction
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jun 4th 2013

I have added the Nadler’s today’s paper at Waldhausen S-construction. It would perhaps make sense to quote it in some more entries.

- Discussion Type
- discussion topicAleksandr Aleksandrov
- Category Latest Changes
- Started by Tim_Porter
- Comments 6
- Last comment by Tim_Porter
- Last Active Jun 3rd 2013

Someone has made a change to the page on Aleksandr Aleksandrov, but there are some characters in the Cyrillic form of his name that are not coming out. Does anyone know how to fix this?

- Discussion Type
- discussion topicGysin/Umkehr/pushforward map in KK-theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 30th 2013

am starting to make some basic notes on Gysin/Umkehr/pushforward maps in KK-theory, currently in

*fiber integration*in the section*In KK-theory*. But still with some gaps.

- Discussion Type
- discussion topicChow group
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active May 30th 2013

started stub for Chow group

hoping I got this right...

- Discussion Type
- discussion topicidempotent completion
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 29th 2013

to

*idempotent completion*(*Karoubi envelope*) I have added :a pointer to further constructions discussed at

*Cauchy complete category*statement of the finality of the completion morphism;

a classical Reference

- Discussion Type
- discussion topich-topology
- Category Latest Changes
- Started by adeelkh
- Comments 2
- Last comment by adeelkh
- Last Active May 28th 2013

- Discussion Type
- discussion topicSmooth loop space
- Category Latest Changes
- Started by Andrew Stacey
- Comments 26
- Last comment by Urs
- Last Active May 27th 2013

Started smooth loop space, initially just a stub. Partly to contain some bits of general theory relating to which smooth paths do I use (davidroberts) and partly to start transferring some notes on the differential topology of loop spaces over to the nLab.

In looking for somewhere to graft it on to the current nLab tree, I encountered loop space object. It seemed to me that the

*smooth*loop space is not a loop space object, so I commented as such (thus also creating the link to smooth loop space which was my real intent). Someone who knows these things better than I do should check this.

- Discussion Type
- discussion topicproduct law
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by TobyBartels
- Last Active May 23rd 2013

created

*product law*, since I wanted to be able to link to it…

- Discussion Type
- discussion topicunintentional type theory
- Category Latest Changes
- Started by Mike Shulman
- Comments 3
- Last comment by TobyBartels
- Last Active May 23rd 2013

Created unintentional type theory.

- Discussion Type
- discussion topictype II supergravity Lie 2-algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 21st 2013

created an entry

*type II supergravity Lie 2-algebra*.

- Discussion Type
- discussion topicindex theory - contents
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 20th 2013

started

*index theory - contents*(somewhat optimistically, for the moment)

- Discussion Type
- discussion topicUnbounded topos
- Category Latest Changes
- Started by DavidRoberts
- Comments 6
- Last comment by TobyBartels
- Last Active May 19th 2013

Created the page unbounded topos, and some links at topos and bounded geometric morphism.

I’m interested in the generalisation of the construction of the unbounded topos $Gl(F)$ to the general case of an inaccessible comonad $G$ on a bounded topos (which wlog we might as well take to be $Set$ EDIT: NO, LET’S NOT). In essence,

*why*is it unbounded? Also, what nice properties can we claim of the category of coalgebras for $G$, given information about $G$.Note also, the paper HOW LARGE ARE LEFT EXACT FUNCTORS? in TAC in 2001 seems to claim something a little stronger than Johnstone does in the Elephant, and recounted at topos, namely that the existence of lex endofunctors of set is independent of ZFC (they say something more general, but it covers this case). This is mostly a note to myself, but if others feel like looking, that would be good too.

- Discussion Type
- discussion topic11d supergravity
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 15th 2013

You may have seen in “Recently revised” that I had edited 11-dimensional supergravity in the last days. I wanted to start a section there on the details of the action functional. But after adding some formulas, I ran out of time and just left an “under construction”-warning.

The reason I ran out of time is that I had to first write related things with higher priority into an article we are currently preparing:

*Multiple M5-branes, String 2-connections, and 7d nonabelian Chern-Simons theory*.Later when the dust has settled and I have more leisure, I’ll try to take care of the $n$Lab’s 11d sugra article again.

- Discussion Type
- discussion topichypercomplete (oo,1)-topos
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active May 14th 2013

added to hypercomplete (infinity,1)-topos a comment on how classical topos theory models these

(motivated from our discussion here)

- Discussion Type
- discussion topicdomain wall, cosmic string, cosmic monopole
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active May 13th 2013

wrote something at

*cosmic string*and by copy-and-pasting-and-changing-the-degrees added something similar to*domain wall*and*monopole*. Needs a bit more polishing, maybe.I am really working on writing out an abstract re-formulation of this classical theory in terms of extended TQFT with defects, but not done with that yet (and will probably be interrupted again before finishing it).

- Discussion Type
- discussion topicFiniteness and ambidexterity in K(n)-local stable homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 13th 2013

Added pointers to

- Jacob Lurie,
*Finiteness and ambidexterity in $K(n)$-local stable homotopy theory*, talk at*Notre Dame Graduate Summer School on Topology and Field Theories*and*Harvard lecture*2012 (video part 1, part 2, part 3 part 4, pdf lecture notes by Chris Elliott)

to relevant entries, such as

*Dijkgraaf-Witten theory*and*Topological Quantum Field Theories from Compact Lie Groups*.- Jacob Lurie,

- Discussion Type
- discussion topicinfinity-Lie algebra cohomology
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 12th 2013

There used to be a warning at infinity-Lie algebra cohomology about whether or not a certain functor needs to be regarded as a derived functor in order to get the correct homotopy-theoretic interpretation of oo-Lie algebroid extensions. I think I have now spelled out at synthetic differential infinity-groupoid the required details and so I replaced that warning with a pointer to a section in that latter entry.

All this can do with a good bit more polishing. I’ll see what I can do eventually.

- Discussion Type
- discussion topicsymplectic connection
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 10th 2013

created

*symplectic connection*, just for completeness at*deformation quantization*

- Discussion Type
- discussion topicLie's first theorem
- Category Latest Changes
- Started by DavidRoberts
- Comments 2
- Last comment by Todd_Trimble
- Last Active May 10th 2013

I added a link to EoM at Lie’s three theorems, where there is a statement of the first theorem - we just had the slightly disparaging sentence

…is today regarded as lacking a good notion of differentiable manifold.

- Discussion Type
- discussion topicTamagawa number
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 10th 2013

stub for

*Tamagawa number*, for the moment just so as to record the article relating it to YM theory.

- Discussion Type
- discussion topicfinite element method
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active May 4th 2013

I archive here the query box from homological algebra and finite element method.

Eric: The appearance of homological algebra in finite element methods goes back a lot earlier than Arnold. It is covered somewhat extensively in Robert Kotiuga’s (who happened to be John Baez’s dorm room mate at MIT) PhD dissertation:

- Kotiuga, P.R., Hodge Decompositions and Computational Electromagnetics, Ph.D. Thesis, McGill University, Montreal, Canada, 1985

I don’t think Robert would claim to be the earliest.

Then you can go back to 1976 with Józef Dodziuk’s classic paper:

- Finite difference approach to the Hodge theory of harmonic forms, Amer. J. Math., 98 (1976), 79-104.

Zoran: Surely, it is emphasised that the numerous precursors exist in the Bulletin survey of Douglas Arnold et al. quoted below. But it was not in any sense systematic till rather recently. One could expand on the history…

I have today posted a question to MathOverflow on recent-fundamental-new-directions-in-pdes.

- Discussion Type
- discussion topicmaximal geodesic (empty?)
- Category Latest Changes
- Started by Tim_Porter
- Comments 2
- Last comment by TobyBartels
- Last Active Apr 30th 2013

Anon. has created an empty maximal geodesic.

- Discussion Type
- discussion topic1-groupoid
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Tim_Porter
- Last Active Apr 29th 2013

The old entry

*1-groupoid*was a bit vague. I have added a paragraph with a more precise description.

- Discussion Type
- discussion topicdiscrete logarithm
- Category Latest Changes
- Started by Tim_Porter
- Comments 2
- Last comment by TobyBartels
- Last Active Apr 28th 2013

Note: Anon… has created discrete logarithm but has not entered any content.

- Discussion Type
- discussion topicconvex cone
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by TobyBartels
- Last Active Apr 26th 2013

I started convex cone. While imitating the link from Jordan algebra to cone, shouldn’t there be a disambiguation between the category theoretic cone and the vector space cone? But even as it is, cone is not that clear on the relation between the cone of homotopy theory and the cone of category theory.

- Discussion Type
- discussion topicnoncommutative geometry - contents
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by zskoda
- Last Active Apr 26th 2013

I am starting a table

*noncommutative geometry - contents*to be included as a “floating table of contents” in the relevant entries.

Clearly this is just a beginning. Zoran will have lots of items to add.

- Discussion Type
- discussion topicSpam attack, deletion of entries
- Category Latest Changes
- Started by Tim_Porter
- Comments 14
- Last comment by Urs
- Last Active Apr 26th 2013

Look at what has been happening at derivator. The entry was erased and various things put there by an Anonymous Coward. Another one has reinstated the original one!! Has anyone noticed this? I was travelling about the time it happened so my usual check did not occur.

At triangle identities something similar had started. I have rolled back.

- Discussion Type
- discussion topicCartan-Eilenberg category
- Category Latest Changes
- Started by zskoda
- Comments 12
- Last comment by jim_stasheff
- Last Active Apr 26th 2013

A stub for Cartan-Eilenberg categories.

- Discussion Type
- discussion topichomotopy n-type - table
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Apr 25th 2013

created a table

*homotopy n-type - table*and included it into the relevant entries