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- Discussion Type
- discussion topicPoincare duality algebra
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jul 16th 2013

I am starting an entry

*Poincaré duality algebra*, but it still needs some attention

- Discussion Type
- discussion topicunitisation of C-star algebras
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 16th 2013

created

*unitisation of C*-algebras*

- Discussion Type
- discussion topicchiral ring
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 16th 2013

stub for

*chiral ring*(not good yet)

- Discussion Type
- discussion topicTarski-Seidenberg theorem
- Category Latest Changes
- Started by Todd_Trimble
- Comments 1
- Last comment by Todd_Trimble
- Last Active Jul 14th 2013

I began to expand Tarski-Seidenberg theorem (formerly a stub) by including some commentary on its significance, and some related results. This is to help create a niche for Schanuel’s conjecture, yet to be written, but which was invoked in a discussion at MO.

- Discussion Type
- discussion topicmetaplectic correction
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jul 14th 2013

stub for

*metaplectic correction*

- Discussion Type
- discussion topicKodaira vanishing theorem
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 12th 2013

brief statement of

*Kodaira vanishing theorem*for the complex geometry case

- Discussion Type
- discussion topicequivariant KK-theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 12th 2013

started a stub

*equivariant KK-theory*with some quick notes. But still very stubby.

- Discussion Type
- discussion topichomotopy colimit
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Andrew Stacey
- Last Active Jul 10th 2013

Wrote a section General weighted colimit formula at homotopy colimit

giving a general formula

spelling out the special case of simplicial diagrams, that reproduces the Bousfield-Kan formula

spelling out the special case of pushout diagrams, that reproduces the formula (or its dual) discussed more in detail in the other examples that were already present

- Discussion Type
- discussion topiccrossed product c*-algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 9th 2013

I tried to collect some references at

*crossed product C*-algebra*on their relation to convolution C*-algebras of action groupoids. But I guess I run out of steam…

- Discussion Type
- discussion topicanalytic assembly map
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 9th 2013

while writing

*Baum-Connes conjecture*I happened to add some stuff to*analytic assembly map*.

- Discussion Type
- discussion topicdirect image with compact supports
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Urs
- Last Active Jul 7th 2013

I have added a new paragraph to direct image about direct image functor with compact support $f_! F$. Eventually I would create a separate entry direct image with compact support, but not yet.

- Discussion Type
- discussion topicdual morphism
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jul 6th 2013

started

*dual morphism*but then began to hesitate: we must have this discussion somewhere already. But where?

- Discussion Type
- discussion topicElementary point-set notion of higher connectedness.
- Category Latest Changes
- Started by TobyBartels
- Comments 5
- Last comment by TobyBartels
- Last Active Jul 6th 2013

Treating locally path-connected spaces as nice topological spaces, we see that nice path-connected spaces are the same as nice connected spaces, and the definition of the latter is more elementary (in point-set topology) than the former. Then nice simply connected spaces are the same as nice unicoherent spaces, which are again more elementary. This should continue for the entire hierarchy of $n$-connected spaces, so I wrote something there about it.

- Discussion Type
- discussion topicintegration theory - contents
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 5th 2013

started a table of contents

*integration theory - contents*and added it as a floating TOC to the relevant entries.(Mostly as a reminder to myself to write more on fiber integration in generalized cohomology…)

- Discussion Type
- discussion topicfuture of stable homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 5th 2013

Added the following to the references at

*stable homotopy theory*and*algebraic topology*:Brief indications of open questions and future directions (as of 2013) of algebraic topology and stable homotopy theory are in

- Tyler Lawson,
*The future*, Talbot lectures 2013 (pdf)

- Tyler Lawson,

- Discussion Type
- discussion topicasymptotic series
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 5th 2013

created

*asymptotic series*

- Discussion Type
- discussion topicprobability amplitudes
- Category Latest Changes
- Started by Tim_Porter
- Comments 4
- Last comment by Urs
- Last Active Jul 4th 2013

Someone started a page called probability amplitudes but with a single word. I have changed that to say the page is empty. (which of course it is not!) as I did not feel competent to write even a stub on that topic.

- Discussion Type
- discussion topicmodels in presheaf toposes
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jul 4th 2013

created

*models in presheaf toposes*with the statement of the fact that T-models in presheaves are presheaves of T-models, at least for T a geometric theory.Added a pointer to this from the corresponding discussion at

*group object*.

- Discussion Type
- discussion topicUniform convergence spaces
- Category Latest Changes
- Started by TobyBartels
- Comments 13
- Last comment by Tim_Porter
- Last Active Jul 3rd 2013

I made a stub uniform convergence space, but I need to read the reference.

- Discussion Type
- discussion topicholographic principle -- table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 2nd 2013

created a table

*holographic principle – table*(meant to show at on glance what the dictionaty is) and included it into the relevant entries.

- Discussion Type
- discussion topicperfect complex
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Jul 2nd 2013

stub for perfect complex

- Discussion Type
- discussion topicKnizhnik-Zamolodchikov connection
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 2nd 2013

I have added to

*Knizhnik-Zamolodchikov connection*a new paragraph in the Idea section:

*Idea – From geometric quantization of Chern-Simons theory*a bunch of commented references

- Discussion Type
- discussion topicAdS/CFT
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by Urs
- Last Active Jul 1st 2013

- Discussion Type
- discussion topicHomotopy groups of connected spaces
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Jul 1st 2013

There was some misnumbering (sometimes off by 1, sometimes reversed) at homotopy group#truncconn, which hopefully I've fixed.

- Discussion Type
- discussion topicodd line
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 30th 2013

added to

*odd line*a brief remark on the nature of its automorphism super-group and the consequences, also added some relevant references.(I feel like I had added this statement to the $n$Lab elsewhere already long time ago, but can’t find it now.)

- Discussion Type
- discussion topicgenerator v. separator and Grothendieck category
- Category Latest Changes
- Started by Tim_Porter
- Comments 11
- Last comment by zskoda
- Last Active Jun 25th 2013

I was fixing some Spam at generator and noticed that Grothendieck category has a link to generator, but shouldn’t this be to separator? I have fixed it so that the term generator in Grothendieck category links to separator.

I tried to clear up some formatting problems / typos at separator. (There is a query near the bottom of the page that seems to still be unanswered.) Can someone glance at the entry to check my reformatting is right as I was on autopilot when doing it!

- Discussion Type
- discussion topicThe denial inequality
- Category Latest Changes
- Started by TobyBartels
- Comments 6
- Last comment by Urs
- Last Active Jun 25th 2013

A short note at denial inequality, since the subject came up. Mike, please check that I used ‘disequality’ correctly.

- Discussion Type
- discussion topicLindenbaum-Tarski and Boolean algebras.
- Category Latest Changes
- Started by Tim_Porter
- Comments 14
- Last comment by TobyBartels
- Last Active Jun 25th 2013

Just now I needed a definition and discussion of term algebra for the new entry on Lindenbaum-Tarski algebra. I noted we have Lindenbaum algebra in several places with no explanation. I am no logician and have very few logic books available. Are these the same and what generality should be used for the term algebra.

I also looked at the entry on Boolean algebra and was a bit surprised to find there was no elementary algebraic version given. This is the (for dummies) version perhaps, but seeing one of the usual algebraic description and examples (although these are in the Wikipedia page I’m sure) might enable the ideas about Heyting algebras, lattices, etc., there to be more useful. I’m not sure what level to pitch any additions to that entry, any ideas or thoughts anyone?

- Discussion Type
- discussion topicLogical connectives
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Jun 25th 2013

Just a stub at logical connective.

- Discussion Type
- discussion topicBaer sum
- Category Latest Changes
- Started by zskoda
- Comments 8
- Last comment by Todd_Trimble
- Last Active Jun 24th 2013

I am going to rewrite a part of the Baer sum, the section “On short exact sequences”, partly following S. MacLane,

*Homology*, 1963 (he does the version for extensions of $R$-modules). I am not fully understanding and would like to discuss the issue, but I think the current notation is a bit hiding. So here is the version of the section before my update, so it can be reversed if somebody not happy:For $0 \to A \to \hat G_{i} \to G \to 0$ for $i = 1,2$ two short exact sequences of abelian groups, their

$\hat G_1 + \hat G_2 \coloneqq +_* \Delta^* \hat G_1 \times \hat G_2$**Baer sum**isThe first step forms the pullback of the short exact sequence along rhe diagonal on $G$:

$\array{ A \oplus A &\to& A \oplus A \\ \downarrow && \downarrow \\ \Delta^* (\hat G_1 \oplus \hat G_2) &\to& \hat G_1 \oplus \hat G_2 \\ \downarrow && \downarrow \\ G &\stackrel{\Delta_G}{\to}& G\oplus G }$The second forms the pushout along the addition map on $A$:

$\array{ A \oplus A &\stackrel{+}{\to}& A \\ \downarrow && \downarrow \\ \Delta^* (\hat G_1 \oplus \hat G_2) &\to& +_* \Delta^*(\hat G_1 \oplus \hat G_2) \\ \downarrow && \downarrow \\ G &\to& G }$

- Discussion Type
- discussion topicRelative Postnikov tower
- Category Latest Changes
- Started by MatanP
- Comments 1
- Last comment by MatanP
- Last Active Jun 24th 2013

I’ve changed Postnikov system definition 2

the part saying

“The map $X \to im_n(f)$ induces an epimorphism on connected components”

to

“The map $X \to im_n(f)$ induces an epimorphism on homotopy groups in degree $n-1$”.

This was a small issue that confused me.

- Discussion Type
- discussion topicaxiom K
- Category Latest Changes
- Started by Tim_Porter
- Comments 5
- Last comment by TobyBartels
- Last Active Jun 22nd 2013

There is a query at axiom K.

- Discussion Type
- discussion topicQuest for Unification
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 21st 2013

added a pointer to the old lecture

- Edward Witten,
*Quest For Unification*, Heinrich Hertz lecture at SUSY 2002 at DESY, Hamburg (arXiv:hep-ph/0207124)

to

*GUT*and*string phenomenology*.- Edward Witten,

- Discussion Type
- discussion topicextensional and intensional type theory
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Mike Shulman
- Last Active Jun 21st 2013

earlier today I had started splitting off entries intensional type theory and extensional type theory from type theory. But then the Lab halted and now it’s left in somewhat stubby form.

- Discussion Type
- discussion topicLimit points
- Category Latest Changes
- Started by TobyBartels
- Comments 12
- Last comment by TobyBartels
- Last Active Jun 21st 2013

I've seen two meanings for this term, and they are both at limit point, along with a family of other terms for various arity classes.

- 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