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- Discussion Type
- discussion topicinduced character
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Mar 1st 2012

Have created induced character.

- Discussion Type
- discussion topicWeyl algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 1st 2012

following what Zoran just did to

*Heisenberg Lie algebra*, I have added to*Weyl algebra*a note in its relation to the former.

- Discussion Type
- discussion topicBoolean hyperdoctrine
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 1st 2012

created an entry

*Boolean hyperdoctrine*, just for completeness and so as to link to Todd’s notes.

- Discussion Type
- discussion topiccoherent hyperdoctrine
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 1st 2012

created

*coherent hyperdoctrine*(Will now try to bring the entry

*hyperdoctrine*itself into a little bit of shape…)

- Discussion Type
- discussion topiccanonical extension
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 1st 2012

I have started an entry

*canonical extension*.But I am only learning about this myself right now. Expert input would be most welcome.

- Discussion Type
- discussion topictable - models for (infinity,1)-operads
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Feb 29th 2012

I am fiddling with an entry

*table - models for (infinity,1)-operads*meant to allow to see 10+ different model categories and their main Quillen equivalences at one glance.I guess there are better ways to typeset this. (Volunteers please feel free to lend a hand!) But for the time being I’ll settle with what I have so far.

- Discussion Type
- discussion topicarithmetic D-module
- Category Latest Changes
- Started by fpaugam
- Comments 5
- Last comment by fpaugam
- Last Active Feb 29th 2012

Added a section arithmetic D-modules. This is the optimal theory for p-adic cohomology of varieties over finite fields, since it has the six operations. This section is complementary to rigid cohomology.

- Discussion Type
- discussion topiccombinatorial group theory
- Category Latest Changes
- Started by Tim_Porter
- Comments 9
- Last comment by Tim_Porter
- Last Active Feb 29th 2012

I have started various entries on parts of combinatorial group theory, including adding to group presentation, and started Tietze transformation.

- Discussion Type
- discussion topicLie 2-algebra
- Category Latest Changes
- Started by Mirco Richter
- Comments 7
- Last comment by Mirco Richter
- Last Active Feb 28th 2012

In

http://ncatlab.org/nlab/show/Lie+2-algebra, at

“… the differential respects the brackets: for all $x \in g_0$ and $h \in g_1$ we have

$\delta [x,h]=[x,\delta h]$…”

is wrong. The equation should be:

$\delta \alpha(x,h) = [x,\delta h]$Since I don’t know if I have the right to change an nLab entry,I post this here as an suggestion.

- Discussion Type
- discussion topicSpecial Delta Spaces
- Category Latest Changes
- Started by MatanP
- Comments 11
- Last comment by MatanP
- Last Active Feb 28th 2012

- Created a new entry on "special $\Delta$-spaces". Does anyone know of a better name?

The entry is poorly edited since I'm not fluent with the iTex syntax.

- Discussion Type
- discussion topicsimplicial complex, quasi-topological space
- Category Latest Changes
- Started by Todd_Trimble
- Comments 7
- Last comment by Todd_Trimble
- Last Active Feb 27th 2012

I made some much-needed corrections at simplicial complex, directed mostly at errors which had been introduced by yours truly. I also created quasi-topological space (the notion due to Spanier).

I haven’t thought this through, but regarding the process of turning a simplicial complex into a simplicial set, the usual sequence of words seems to involve putting a non-canonical ordering on the set of vertices and then getting ordered simplices from that. But is there anything “wrong” with taking the composite

$SimpComp \hookrightarrow Set^{Fin_{+}^{op}} \stackrel{Set^{i^{op}}}{\to} Set^{\Delta^{op}}$where the inclusion is the realization of simplicial complexes as concrete presheaves on nonempty finite sets, and the second arrow is pulling back along the forgetful functor $i$ from nonempty totally ordered finite sets to nonempty finite sets? This looks much more canonical.

- Discussion Type
- discussion topicarithmetic Chow group
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Feb 27th 2012

prompted by this G+ post by David Roberts, I have started an entry

*arithmetic Chow group*.

- Discussion Type
- discussion topicsymplectomorphism
- Category Latest Changes
- Started by Todd_Trimble
- Comments 1
- Last comment by Todd_Trimble
- Last Active Feb 26th 2012

I hope Urs doesn’t mind my inserting a not-too-serious but nevertheless amusing example at symplectomorphism.

- Discussion Type
- discussion topiclawvere theory
- Category Latest Changes
- Started by Tim_Porter
- Comments 2
- Last comment by Todd_Trimble
- Last Active Feb 26th 2012

Someone set up lawvere theory, but did not add anything to it. They had previously done an edit to FinSet. The new page has a redirect from Lawvere+theory, so I don’t see what 88.104.160.245 is doing. Can someone check the edit at [[FinSet]. It looks as if the person knows some things and so has added a bit, but it is so long since I knew that stuff well so I cannot tell if it is a valid edit or not.

- Discussion Type
- discussion topicVolodin
- Category Latest Changes
- Started by Tim_Porter
- Comments 2
- Last comment by TobyBartels
- Last Active Feb 26th 2012

I have created a stub on Volodin. I have been unable to find out more on him. Can anyone help?

- Discussion Type
- discussion topicpresentation of a category by generators and relations
- Category Latest Changes
- Started by Yaron
- Comments 5
- Last comment by TobyBartels
- Last Active Feb 26th 2012

Started presentation of a category by generators and relations. This is probably an evil definition (there was an old discussion on this in the context of quotient category), and there is perhaps a more modern way to do this, so feel free to change the entry. I used “quotient category” as in CWM and mentioned that this is not the definition in the nLab.

- Discussion Type
- discussion topicVietoris complex
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Feb 25th 2012

I have added some material into Vietoris complex relating to links with algebraic K-theory and some conjectures of Kapranov and Saito.

- Discussion Type
- discussion topiccohesive étale ∞-groupoid
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Stephan A Spahn
- Last Active Feb 24th 2012

The last two days Stephan Spahn was visiting me, and we chatted a lot about étaleness in cohesive ∞-toposes.

We found proofs that

for every notion of infinitesimal cohesive neighbourhood

$i : \mathbf{H} \hookrightarrow \mathbf{H}_{th}$the total space projections of locally constant $\infty$-stacks are formally étale;

the formally étale morphisms with respect to any choice of infinitesimal cohesion satisfy all the axioms of axiomatic open maps (or rather their $\infty$-version, of course).

(These are to be written up. Requires plenty of 3d iterated $\infty$-pullback diagrams which are hard to typeset).

Recall – from synthetic differential infinity-groupoid – that for the infinitesimal cohesive neighbourhood

$i :$ Smooth∞Grpd $\hookrightarrow$ SynthDiff∞Grpd

the axiomatically formally étale morphisms between smooth manifolds are precisely the étale maps in the traditional sense.

Motivated by all this, I finally see, I think, what the correct definition of

*cohesive étale ∞-groupoid*is:simply: $X \in \mathbf{H}$ is an étale cohesive $\infty$-groupoid if it admits an atlas $X_0 \to X$ by a formally étale morphism in $\mathbf{H}$.

I have spelled out the proof now here that with this definition a Lie groupoid $\mathcal{G}$ is an étale groupoid in the traditional sense, precisely if it is cohesively étale when regarded as an object of the infinitesimal cohesive neighbourhood $Smooth \infty Grpd \hookrightarrow SynthDiff \infty Grpd$.

I hope to further expand on all this with Stephan. But I may be absorbed with other things. Next week I am in Goettingen, busy with a seminar on $L_\infty$-connections.

- Discussion Type
- discussion topicbasis of a vector space
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by TobyBartels
- Last Active Feb 23rd 2012

I found in the disambiguation page basis an entry

*basis of a vector space*missing, and so I created one. I have then cross-linked this with relevant existing entries, such as basis theorem. Also created a brief entry orthogonal basis in order to get rid of grayish links is some entries.

- Discussion Type
- discussion topicrelatively k-compact morphism
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 1
- Last comment by Stephan A Spahn
- Last Active Feb 23rd 2012

In context of size issues on admissible structures (in the sense of DAG V) I wondered which closure properties (e.g. obviously its closed under pullbacks along relatively k-compact morphisms) the class of relatively k-compact (for a regular cardinal k) morphisms in a (∞,1)-category satisfies. Is there any reference concerning this?

- Discussion Type
- discussion topicdendroidal set
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Feb 23rd 2012

added at dendroidal set

a section on the relation to simplicial sets

a section on the symmetric monoidal structure on the cat of dendroidal sets

(also added a stubby "overview" section to model structure on dendroidal sets)

- Discussion Type
- discussion topictwisted K-homology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 22nd 2012

I needed an entry that lists references on

*twisted K-homology*, so I created one. This made me notice that we currently lack an entry*K-homology*. I can try to create a stub for that a little later…

- Discussion Type
- discussion topicsaturated classes of limits
- Category Latest Changes
- Started by Mike Shulman
- Comments 2
- Last comment by Mike Shulman
- Last Active Feb 22nd 2012

Created saturated class of limits.

- Discussion Type
- discussion topicsymplectic singularity
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Ben Webster
- Last Active Feb 22nd 2012

created

*symplectic singularity*…… for the moment just to record references and such as to satisfy links at

*symplectic duality*.

- Discussion Type
- discussion topicCharles Wells
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by TobyBartels
- Last Active Feb 22nd 2012

the link to the picture in the entry

*Charles Wells*is broken. Does anyone know how to fix it or have an alternative picture?

- Discussion Type
- discussion topicadjoint representation
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 18th 2012

stub for

*adjoint representation*

- Discussion Type
- discussion topicKoszul
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by Tim_Porter
- Last Active Feb 18th 2012

Perhaps we need a page on Jean-Louis Koszul, and possibly an agreement on terminology / names for entries. Ben has created a page called Koszul, but usually single names like that would be used for the ’person’ page of that mathematician, so … The term in in any case (as adjective) is also used in various other contexts e.g. for operads, so possibly there needs to be some rationalisation. My thought would be to combine a page on Koszul (and the Wikipedia (English) page on him is poor, and includes some very poor translation from the French ) with a certain amount of disambiguation, however I am not an expert on things ’Koszul’ and this may not be the most efficient way to go.

- Discussion Type
- discussion topicorbifold groupoids
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 2
- Last comment by Mike Shulman
- Last Active Feb 17th 2012

I created orbifold groupoids with some classes of groupoids whose elements I like to think of as ‘‘orbifold groupoids‘‘. It would be nice to have a discussion of the interelation of these classes there, too.

- Discussion Type
- discussion topicgeometry (for structured (infinity,1)-toposes)
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Feb 16th 2012

I rewrote the Idea-section of geometry (for structured (infinity,1)-toposes), tring to make it more to the point and much shorter. Also highlighted the relation to oo-algebraic theories.

- Discussion Type
- discussion topiccanonical model structure on Operad
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 15th 2012

quick note

*canonical model structure on Operad*.Needs to be expanded and equipped with commented cross-links to the related entries. Later.

- Discussion Type
- discussion topicBeilinson-Deligne cup product
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by domenico_fiorenza
- Last Active Feb 15th 2012

added the definition to Beilinson-Deligne cup product.

Also expanded the list of references here and at Deligne cohomology.

- Discussion Type
- discussion topicoperadic (∞,1)-Grothendieck construction
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 15th 2012

am starting an entry

*operadic (∞,1)-Grothendieck construction*

- Discussion Type
- discussion topicPi-closed morphism
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 8
- Last comment by Urs
- Last Active Feb 15th 2012

I created Pi-closed morphism. This material is in differential cohomology in a cohesive (∞,1)-topos, too.

- Discussion Type
- discussion topicCartesian fibration of dendroidal sets
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 14th 2012

am starting an entry

*Cartesian fibration of dendroidal sets*

- Discussion Type
- discussion topicfibration of multicategories
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 14th 2012

I was in the process of creating an entry for

*Cartesian fibration of dendroidal sets*, when by accident I suddently discovered that the degree-1 case of this had been considered before, by Claudio Hermida. So now I have also created a brief entry

- Discussion Type
- discussion topicsuper parallel transport
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 14th 2012

created a stub for super parallel transport, for the moment just so as to record Florin Dumitrscu’s recent preprint

- Discussion Type
- discussion topicassociative operad
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Stephan A Spahn
- Last Active Feb 14th 2012

at

*associative operad*I have made explict the links to*symmetric operad*and*planar operad*, as need be.

- Discussion Type
- discussion topicsymmetric operad
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Feb 13th 2012

I thought it would be useful to supplement the entry

*operad*with entries*symmetric operad*and*planar operad*, that amplify a bit more on the specifics of these respective flavors of the general notion, and that will allow us in other entries to link specifically to one of the two notions, when the choice is to be made explicit.So far I have written (only) an Idea-section at

*symmetric operad*with some comments.To be expanded.

- Discussion Type
- discussion topicBoardman-Vogt tensor product
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Feb 13th 2012

started an entry on the

*Boardman-Vogt tensor product*on symmetric colored operads.

- Discussion Type
- discussion topicparity complex
- Category Latest Changes
- Started by Todd_Trimble
- Comments 4
- Last comment by Todd_Trimble
- Last Active Feb 12th 2012

Started the article parity complex.

- Discussion Type
- discussion topiciterated loop space object
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 9th 2012

I have created a bunch of stub entries such as

*iterated loop space object*with little non-redundant content for the moment. I am filling the k-monoidal table. Please bear with me for the time being, while I add stuff.

- Discussion Type
- discussion topick-monoidal table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 9th 2012

have created an entry

*k-monoidal table*to be used for inclusion into the entries that it organizes (see for instance at*infinite loop space*).Will now create at least stubs for the missing links.

- Discussion Type
- discussion topicSteinberg group.
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Feb 9th 2012

I have created an entry on the Steinberg group $St(R)$ of a ring $R$. The entry includes the Whitehead lemma.

- Discussion Type
- discussion topicKac-Moody algebra
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by zskoda
- Last Active Feb 8th 2012

I have half-heartedly started adding something to

*Kac-Moody algebra*. Mostly refrences so far. But I don’t have the time right now to do any more.

- Discussion Type
- discussion topicoperator topology
- Category Latest Changes
- Started by zskoda
- Comments 7
- Last comment by zskoda
- Last Active Feb 8th 2012

New entries operator topology (for now redirecting also strong operator topology etc.) and unitary representation. Changes at projection measure (the sigma algebra does not need to be the sigma algebra of Borel subsets on a topological space!) and spectral measure. At some point one should add some crosslinks from/to other entries in functional analysis but I am on slow/expensive connection now, hence will restrain to more substantial (in content sense) edits.

- Discussion Type
- discussion topicKan extension
- Category Latest Changes
- Started by fpaugam
- Comments 3
- Last comment by fpaugam
- Last Active Feb 7th 2012

- Is the notion of local Kan extension in weak or infinity n-categories well defined. I know there is the infinity,1-case done by Lurie, but it is not local. I would define a Kan extension as the datum of a 1-morphism filling the usual diagram, with a 2-morphism that induces an equivalence of (n-2)-categories of morphisms between morphisms. You may do the same in the infinity,n case, if needed.

Is there a better definition?

The point is to define limits in weak n-categories using this. It is not simpler to define limit than to define Kan extensions.

Are there finer notions of local extensions, that use more explicitely the higher category structure?

- Discussion Type
- discussion topiccoproduct-preserving representable
- Category Latest Changes
- Started by Todd_Trimble
- Comments 12
- Last comment by Tim_Porter
- Last Active Feb 7th 2012

Labbified an MO discussion at coproduct-preserving representable.

- Discussion Type
- discussion topicidentity component
- Category Latest Changes
- Started by Todd_Trimble
- Comments 1
- Last comment by Todd_Trimble
- Last Active Feb 3rd 2012

Created identity component, and added some little remarks to open map and quotient space.

- Discussion Type
- discussion topicQuillen plus construction
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Feb 3rd 2012

I have started a stub on this. (Isn’t there a nice nPOV interpretation of this?)

- Discussion Type
- discussion topicHigher doctrines
- Category Latest Changes
- Started by fpaugam
- Comments 29
- Last comment by Mike Shulman
- Last Active Feb 3rd 2012

- A new contribution

- Discussion Type
- discussion topicalmost connected topological group
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Feb 2nd 2012

just for completeness, I have created an entry

*almost connected topological group*.

- Discussion Type
- discussion topiccubical set
- Category Latest Changes
- Started by Tim_Porter
- Comments 25
- Last comment by Todd_Trimble
- Last Active Feb 2nd 2012

There is a strange glitch on this page: the geometric realization of a cubical set (see geometric realizationealization) below) tends to have the wrong homotopy type:

That is what appears but is not a t all what the source looks like:

the geometric realization of a cubical set (see [geometric realization](#geometric realization) below) tends to have the wrong homotopy type:

What is going wrong and how can it be fixed?

Another point : does anyone know anything about symmetric cubical sets?

- Discussion Type
- discussion topicnormal morphism of infinity-groups
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Feb 2nd 2012

Added to

*normal subgroup*a section*Normal morphisms of ∞-groups*.

- Discussion Type
- discussion topicexceptional geometry
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 1st 2012

I am slowly starting to add stuff at

*exceptional geometry*

- Discussion Type
- discussion topicclassifying topos
- Category Latest Changes
- Started by Todd_Trimble
- Comments 25
- Last comment by Mike Shulman
- Last Active Feb 1st 2012

I made some edits at classifying topos to correct what I thought were some inaccuracies. One is that simplicial sets classify interval objects, but offhand I didn’t see the exact notion of linear interval over at interval object that would make this a correct sentence. In any event, I went ahead and defined the notion of linear interval as a model of a specified geometric theory.

The other is for local rings. I think when algebraic geometers refer to a sheaf of local rings, they refer to a sheaf of rings over a (sober) space all of whose stalks are local. I wasn’t sure that description would be kosher for a general (Grothendieck) topos $E$ since there may not be any “stalks” (i.e., points $Set \to E$) to refer to. In any case, it seems to me safer to give the geometric theory directly.

- Discussion Type
- discussion topicmodel structure on cosimplicial simplicial sets
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 31st 2012

Matan Prezma kindly pointed out the he has an article with a correction to what used to be prop. 2 at

*model structure on cosimplicial simplicial sets*. (One has to use restricted totalization instead of ordinary totalization.)I have corrected this and added the reference.

I also added to the entry a remark that makes the relation to descent objects explicit. Right now this is remark 2.

- Discussion Type
- discussion topicsubgroup
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 31st 2012

at

*subgroup*I have collected a list of links to $n$Lab entries of the form “xyz subgroup”. If anyone knows of more such entries (or does a more thorough search), please consider adding them!

- Discussion Type
- discussion topiccone
- Category Latest Changes
- Started by Eric
- Comments 11
- Last comment by Urs
- Last Active Jan 30th 2012

Added a diagram to cone and changed some notation to be compatible with cone morphism and Understanding Constructions in Set

- Discussion Type
- discussion topictrivial and mixed model structures
- Category Latest Changes
- Started by Mike Shulman
- Comments 3
- Last comment by Mike Shulman
- Last Active Jan 28th 2012

New pages: 2-trivial model structure and mixed model structure.

- Discussion Type
- discussion topicbialgebra vs. GS cohomology
- Category Latest Changes
- Started by fpaugam
- Comments 17
- Last comment by zskoda
- Last Active Jan 27th 2012

- How is Majid's bialgebra cohomology related to GS cohomology for bialgebras?

I saw the recent paper by Shoikhet where GS cohomology is k-monoidally understood.

Is there a similar understanding of Majid's cohomology?