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- 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 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 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?

- Discussion Type
- discussion topicfactorization system over a subcategory
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Jan 27th 2012

New page factorization system over a subcategory.

- Discussion Type
- discussion topicMeasurable stuff
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Jan 22nd 2012

Split measurable subset and measurable function (unfinished) from sigma-algebra and measurable space. Also added to sigma-ideal. Still need to split some things from measure space.

- Discussion Type
- discussion topicSuslin
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by Tim_Porter
- Last Active Jan 21st 2012

I have created a stub entry for A. Suslin. Can someone add in the Russian original of his name please, as I do not know if the Wikipedia version is correct?

- Discussion Type
- discussion topicCheng measurable spaces
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by TobyBartels
- Last Active Jan 21st 2012

Some time ago, I split Cheng space from measurable space, but I never announced it here (nor removed if from the list of things to do at the latter). Note: Henry Cheng, not Eugenia Cheng.

- Discussion Type
- discussion topicCharacters of profinite groups
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Jan 20th 2012

I added a brief equivalence between two notions of characters of profinite groups that I spotted on MO.

- Discussion Type
- discussion topicextremum
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by TobyBartels
- Last Active Jan 20th 2012

looks like I started

*extremum*(I wanted

*minimum*not to be gray at higher dimensional Chern-Simons theory…)

- Discussion Type
- discussion topicscissors congruence
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jan 19th 2012

New entry scissors congruence.

- Discussion Type
- discussion topicsome classifying toposes
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Jan 17th 2012

I added a section to simplicial set remarking on their status as a classifying topos, and a sentence to classifying topos (in the section “For objects”) recording the answer to this question.

- Discussion Type
- discussion topicWu class
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 16th 2012

I have created an entry

*Wu class*.At the end I have also included an “Applications”-section with comments on Wu classes in the definition of higher Chern-Simons functionals. That eventually deserves to go in a dedicated entry, but for the moment I think it is good to have it there, as it is a major source of discussion of Wu structures in the maths literature, quite indepently of its role in physics.

- Discussion Type
- discussion topic''(-) object vs. internal (-)''
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 11
- Last comment by Stephan A Spahn
- Last Active Jan 15th 2012

I added links to the horizontal categorifications in group object and created groupoid object.

In groupoid object in an (infinity,1)-category I read the conspicious statement: ”an internal ∞-group or internal ∞-groupoid may be defined as a group(oid) object internal to an (∞,1)-category C with pullbacks” - but this terminology seems to hinder distinguishing between them and ∞-groupoid objects in (∞,1)-categories.

- Discussion Type
- discussion topicScone
- Category Latest Changes
- Started by David_Corfield
- Comments 11
- Last comment by Mike Shulman
- Last Active Jan 13th 2012

After Mike’s post, scone was created. But I see at Freyd cover it says

The Freyd cover of a category – sometimes known as the Sierpinski cone or “scone” – is a special case of Artin gluing

Are they synonyms?

- Discussion Type
- discussion topicdescent and locality - contents
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by Urs
- Last Active Jan 13th 2012

Have created a table of contents

*descent and locality - contents*.Am including this now as a “floating TOC” into the relevant entries.

- Discussion Type
- discussion topicAlfsen-Shultz theorem
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 13th 2012

I am just hearing about the Alfsen-Shultz theorem about states on C*-algebras, so I started a stub to remind me. Still need to track down the reference and the details.

- Discussion Type
- discussion topicLocales
- Category Latest Changes
- Started by TobyBartels
- Comments 4
- Last comment by Mike Shulman
- Last Active Jan 11th 2012

I went through locale and made some of the language consistent throughout the article. Also I added a new section, Subsidiary notions, to which I intend to add.

- Discussion Type
- discussion topicToposes
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jan 11th 2012

started a stub entry Toposes on the category (2-category) of all toposes. But nothing much there yet.

- Discussion Type
- discussion topicrelative cohomology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 9th 2012

I have put some content into the entry

*relative cohomology*

- Discussion Type
- discussion topicanalytic manifold
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Jan 9th 2012

stub for analytic manifold

- Discussion Type
- discussion topicboundary of a simplex
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 1
- Last comment by Stephan A Spahn
- Last Active Jan 8th 2012

I added the coequalizer description of a boundary of a simplex. The horn has such a description, too…

- Discussion Type
- discussion topicnerve and realization
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 2
- Last comment by Urs
- Last Active Jan 8th 2012

I inserted two links in nerve and realization: simplicial topological space (redirecting cosimplicial topological space) and geometric realization of simplicial topological spaces. I would like to add some remarks to the internal case.

- Discussion Type
- discussion topicLanglands correspondence -- contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 7th 2012

when creating a stub entry

*local Langlands conjectures*I noticed that it has already become hard to know which entries on the Langlands program we already have. I always take this as a sign that a summary table of contents is called for. So I startedLanglands correspondence – contents

and added it as a “floating table of contents” to the relevant entries.

(Even though all of these entries are still more or less stubs.)

- Discussion Type
- discussion topicbuilding
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 6th 2012

I noticed that there was some wild formatting at

*building*. I have tried to tame it a bit.

- Discussion Type
- discussion topicnon-commutative analytic space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 6th 2012

a reference on non-commutative analytic spaces (Berkovich style)

- Discussion Type
- discussion topicanalytic spectrum
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 4th 2012

started analytic spectrum (redirecting Berkovich spectrum)

- Discussion Type
- discussion topicmeasure theory - contents
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Jan 4th 2012

I have started a table of contents measure theory - contents and started adding it as a floating toc to the relevant entries

- Discussion Type
- discussion topicArchimedean field
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 4th 2012

- Discussion Type
- discussion topicNori motives
- Category Latest Changes
- Started by zskoda
- Comments 4
- Last comment by zskoda
- Last Active Jan 4th 2012

- Discussion Type
- discussion topicanalytic geometry
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by zskoda
- Last Active Jan 4th 2012

currently the bulk of the entry analytic geometry is occupied by a long section on “Holomorphic functions of several complex variables”. Should that not better be moved to some dedicated entry of its own? Any opinions?

- Discussion Type
- discussion topicbranched manifold
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 4
- Last comment by Urs
- Last Active Jan 3rd 2012

I created branched manifold -linked from orbifold- with a definition from ”expanding attractors” by Robert F. Williams (1974) quoted in wikipedia. This description is -as it stands- not precisely compatible to that given in Dusa McDuffs ”Groupoids, Branched Manifolds and Multisections” which I am rather interested in. So I plan to comment on this as a side note in the -yet to be written-article orbifold groupoid.

- Discussion Type
- discussion topicdescent algebra
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jan 3rd 2012

A stub for the famous Solomon’s descent algebra.

- Discussion Type
- discussion topiccategory with weak equivalences
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Mike Shulman
- Last Active Jan 3rd 2012

I have a further comment/question in the query box at category with weak equivalences

- Discussion Type
- discussion topicCofinality
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by TobyBartels
- Last Active Jan 1st 2012

New article: cofinality, with the basic case being the cofinality of a quasiorder as a collection of cardinal numbers, a variation as a collection of ordinal numbers (or equivalently an ordinal number), and an apparently separate case of the cofinality of a collection of cardinal numbers, all of these tied together and interpreted as a single cardinal number if one assumes the axiom of choice.

- Discussion Type
- discussion topicMayer-Vietoris sequence
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Dec 31st 2011

created Mayer-Vietoris sequence

- Discussion Type
- discussion topicdiffemorphism group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 31st 2011

added to diffeomorphism group statements and references for the case of 3-manifolds (Smale conjecture etc.)

- Discussion Type
- discussion topictwisted spin^c structure
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 30th 2011

I added four more references at twisted spin^c structure (aka “Freed-Witten anomaly cancellation”) after A clean formulation and review is provided in….

- Discussion Type
- discussion topicfinite (infinity,1)-limit
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Dec 23rd 2011

I was surprised to discover that we had no page finite (infinity,1)-limit yet, especially given that they are slightly subtle in relation to the 1-categorical version. So I made one.

- Discussion Type
- discussion topicintuitionistic logic
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 22nd 2011

I have added the Tarski reference to intuitionistic logic and internal logic

- Discussion Type
- discussion topicsupercompact cardinal
- Category Latest Changes
- Started by DavidRoberts
- Comments 1
- Last comment by DavidRoberts
- Last Active Dec 22nd 2011

From supercompact cardinal:

**Theorem:**The existence of arbitrarily large supercompact cardinals implies the statement:Every absolute epireflective class of objects in a balanced accessible category is a small-orthogonality class.

In other words, if $L$ is a reflective localization functor on a balanced accessible category such that the unit morphism $X \to L X$ is an epimorphism for all $X$ and the class of $L$-local objects is defined by an absolute formula, then the existence of a suficciently large supercompact cardinal implies that $L$ is a localization with respect to some set of morphisms.

This is in

*BagariaCasacubertaMathias*Urs Schreiber: I am being told in prvivate communication that the assumption of epis can actually be dropped. A refined result is due out soon.

does anyone know about this refined result?

- Discussion Type
- discussion topiclocalizing subcategory
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by zskoda
- Last Active Dec 21st 2011

this is a message to Zoran:

I have tried to refine the section-outline at localizing subcategory a bit. Can you live with the result? Let me know.

- Discussion Type
- discussion topicfull functor
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 21st 2011

discovered the following remnant discussion at full functor, which hereby I move from there to here

*Mathieu says:*I agree that, for functors, there is no reason to say “fully faithful” rather than “full and faithful”. But for arrows in a 2-category (like in the new version of the entry on subcategories), there are reasons. I quote myself (from my thesis): «Remark: we say*fully faithful*and not*full and faithful*, because the condition that, for all $X:\C$, $C(X,f)$ be full is not equivalent in $\Grpd$ to $f$ being full. Moreover, in $\Grpd$, this condition implies faithfulness. We will define (Definition 197) a notion of full arrow in a $\Grpd$-category which, in $\Grpd$ and $\Symm2\Grp$ (symmetric 2-groups), gives back the ordinary full functors.» Note that this works only for some good groupoid enriched categories, not for $\Cat$, for example.*Mike*says: Do you have a reason to care about full functors which are not also faithful? I’ve never seen a very compelling one. (Maybe I should just read your thesis…) I agree that “full morphism” (in the representable sense) is not really a useful/correct concept in a general 2-category, and that therefore “full and faithful” is not entirely appropriate, so I usually use “ff” in that context. I’ve changed the entry above a bit to reflect your comment; is it satisfactory now? Maybe all this should actually go at full and faithful functor (and/or fully faithful functor)?

- Discussion Type
- discussion topicline object
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Dec 21st 2011

created line object