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- Discussion Type
- discussion topichomotopy group
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Aug 31st 2012

I have added to homotopy group a very brief pointer to Mike’s HoTT formalization of $\pi_1(S^1)$.

Eventually I would like to have by default our $n$Lab entries be equipped with detailed pointers to which aspects have been formalized in HoTT (if they have), and in which .v-file precisely.

- Discussion Type
- discussion topicprojective object
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Aug 30th 2012

I added some first statements about projective resolutions also to

*projective object*.

- Discussion Type
- discussion topicprojective presentation
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 30th 2012

felt the need to have a quick entry

*projective presentation*.

- Discussion Type
- discussion topicgroup theory - contents
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Aug 30th 2012

I have started a floating table of contents group theory - contents, and started adding it to some relevant entries

(the toc is neither meant to already be complete nor to be optimally organized, please expand and polish as you see the need)

- Discussion Type
- discussion topicUniversal coefficient theorems
- Category Latest Changes
- Started by Andrew Stacey
- Comments 22
- Last comment by Andrew Stacey
- Last Active Aug 30th 2012

I was reading Adams’ lectures on generalised cohomology theories and added some stuff from there to universal coefficient theorem about the more general case (including the Kunneth theorem).

- Discussion Type
- discussion topicSequence spaces
- Category Latest Changes
- Started by TobyBartels
- Comments 9
- Last comment by Tom Leinster
- Last Active Aug 30th 2012

Another new article: sequence space. I await the inevitable report that this term is also used for other things.

- Discussion Type
- discussion topicBanach coalgebras
- Category Latest Changes
- Started by TobyBartels
- Comments 26
- Last comment by TobyBartels
- Last Active Aug 28th 2012

New page: Banach coalgebra.

Hopefully you all know that $l^1$ is a Banach

*algebra*under*convolution*, but did you know that $l^\infty$ is a Banach*coalgebra*under*nvolution*? (Actually, they are both Banach bialgebras!)

- Discussion Type
- discussion topiccompactly generated triangulated category
- Category Latest Changes
- Started by Karol Szumiło
- Comments 4
- Last comment by Mike Shulman
- Last Active Aug 28th 2012

- I have created compactly generated triangulated category and most probably violated many of your formatting and typesetting conventions...

- Discussion Type
- discussion topicelement in an abelian category
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by IngoBlechschmidt
- Last Active Aug 28th 2012

I added an Idea-section to

*element in an abelian category*and added a reference by George Bergman.This links back to the new Idea section at abelian categories - embedding theorems. Check if you agree with the wording.

- Discussion Type
- discussion topicpre-abelian category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 27th 2012

I have touched the formatting at

*pre-abelian category*.

- Discussion Type
- discussion topicchain homology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 27th 2012

I have added to the entry

*chain homology and cohomology*an actual Idea-section and an actual definition. The material that used to be there I have moved into a section*Chain homology – In the context of homotopy theory*.

- Discussion Type
- discussion topicThompson's group F
- Category Latest Changes
- Started by Mike Shulman
- Comments 3
- Last comment by Mike Shulman
- Last Active Aug 27th 2012

stub for Thomspon’s group F.

- Discussion Type
- discussion topicchains and cochains - table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 26th 2012

created a little table:

*chains and cochains - table*and included it into the relevant entries (some of which still deserve to be edited quite a bit).

- Discussion Type
- discussion topicunimodular lattice
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 25th 2012

discussion over in the thread on

*modular lattice*keeps making me create stub likes*unimodular lattice*and*Leech lattice*. No genuine content there yet, though. It just seems necessary to have these entries at all.

- Discussion Type
- discussion topicHeisenberg Lie n-algebra
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Aug 25th 2012

I am splitting off

*Heisenberg Lie n-algebra*from*Heisenberg Lie algebra*.

- Discussion Type
- discussion topicrelations - contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 24th 2012

I have created a table

*relations - contents*and added it as a floatic TOC to the relevant entries.

- Discussion Type
- discussion topicsnake lemma
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Aug 24th 2012

statement of the

*snake lemma*

- Discussion Type
- discussion topiccohomology theory
- Category Latest Changes
- Started by Mike Shulman
- Comments 25
- Last comment by TobyBartels
- Last Active Aug 24th 2012

Is there a reason for the page cohomology theory to exist independently, rather than as a redirect to generalized (Eilenberg-Steenrod) cohomology?

- Discussion Type
- discussion topicdelta-functor
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 24th 2012

Created

*delta-functor*.(also touched

*Tohoku*, adding hyperlinks and “the”-s)

- Discussion Type
- discussion topicbornological set
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by TobyBartels
- Last Active Aug 23rd 2012

I added a few observations under a new section “Results” at bornological set. Bornological sets form a quasitopos. I don’t have a good reference for the theorem of Schanuel.

Related is an observation which hadn’t occurred to me before: the category of sets equipped with a reflexive symmetric relation is a quasitopos. I’d like to return to this sometime in the context of thinking about morphisms of (simple) graphs.

- Discussion Type
- discussion topic(infinity,n)-category with adjoints
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 23rd 2012

I have started an entry

*(∞,n)-category with adjoints*, prompted by wanting to record these slides:- Nick Rozenblyum,
*Manifolds, Higher Categories and Topological Field Theories*, talk Northwestern University (2012) (pdf slides)

If anyone can say more about the result indicated there, I’d be most grateful for a comment.

Also, I seem to hear that at Luminy 2012 there was some extra talk, not appearing on the schedule (maybe by Nick Rozenblyum, but I am not sure) on something related to

*geometric quantization*. If anyone has anything on that, I’d also be most grateful.- Nick Rozenblyum,

- Discussion Type
- discussion topicDual spaces
- Category Latest Changes
- Started by TobyBartels
- Comments 11
- Last comment by TobyBartels
- Last Active Aug 22nd 2012

New page dual space with redirect from dual basis.

- Discussion Type
- discussion topicstring
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 22nd 2012

in the entry

*string*I have started adding*References on symplectic geometry and geometric quantization*of the string sigma-model

- Discussion Type
- discussion topic2-plectic geometry
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 22nd 2012

I am splitting off

*2-plectic geometry*from*n-plectic geometry*.

- Discussion Type
- discussion topicadditive and abelian categories - contents
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Aug 20th 2012

I created another floating TOC

*additive and abelian categories - contents*and added it to the relevant entries

- Discussion Type
- discussion topicduality - contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 20th 2012

I am starting a table of contents, to be included as a floating TOC for entries related to duality:

But it’s a bit rough for the time being. I haven’t decided yet how to best organize it and I am probably still lacking many items that deserve to be included. To be developed. All input is welcome.

- Discussion Type
- discussion topicproduct-preserving functor
- Category Latest Changes
- Started by Todd_Trimble
- Comments 10
- Last comment by DavidRoberts
- Last Active Aug 19th 2012

Created product-preserving functor.

- Discussion Type
- discussion topicDirects sums of Banach spaces
- Category Latest Changes
- Started by TobyBartels
- Comments 12
- Last comment by TobyBartels
- Last Active Aug 18th 2012

New article: direct sum of Banach spaces. These come in even more variety than I originally thought!

- Discussion Type
- discussion topicShort linear maps
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Aug 16th 2012

I got tired of writing ‘short linear map’, so now we have short linear map.

- Discussion Type
- discussion topicfunction application
- Category Latest Changes
- Started by Mike Shulman
- Comments 10
- Last comment by Todd_Trimble
- Last Active Aug 16th 2012

I created function application, so as to be able to link to it from fixed-point combinator. While adding links, I was motivated to expand a bit on function.

- Discussion Type
- discussion topicdual object in a closed monoidal category
- Category Latest Changes
- Started by Todd_Trimble
- Comments 16
- Last comment by TobyBartels
- Last Active Aug 14th 2012

- Discussion Type
- discussion topicZ_infinity-modules
- Category Latest Changes
- Started by Zhen Lin
- Comments 4
- Last comment by Urs
- Last Active Aug 13th 2012

I started the article Z-infinity-module. Hopefully someone here can say something more interesting about them!

- Discussion Type
- discussion topicadjoint equivalence
- Category Latest Changes
- Started by Mike Shulman
- Comments 6
- Last comment by Mike Shulman
- Last Active Aug 13th 2012

I added some remarks to adjoint equivalence about improving equivalences to adjoint ones, with links to&from equivalence and equivalence in a quasicategory.

- Discussion Type
- discussion topicRiesz representation theorems
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by Urs
- Last Active Aug 12th 2012

I'm putting all the big duality theorems from measure theory at Riesz representation theorem. Only a couple are filled in so far, but I'm out of time for today.

- Discussion Type
- discussion topicSpam and other types of 'interference'
- Category Latest Changes
- Started by Tim_Porter
- Comments 8
- Last comment by Tim_Porter
- Last Active Aug 8th 2012

There have been several entries with no math content recently. What is the procedure? I am meaning: Search results for definion and The Enemy of my Enemy is not my Friend.

- Discussion Type
- discussion topicProblems with all pages on dependent type theory
- Category Latest Changes
- Started by Harry Gindi
- Comments 10
- Last comment by Mike Shulman
- Last Active Aug 7th 2012

Heya. I haven’t actually made the necessary changes, but the various pages on dependent type theory make the statement that every DTT or MLTT is the internal logic of an LCCC and every LCCC is the categorical semantics of some DTT/MLTT. However, this is extremely confusing (it took me 2 or 3 hours to find a page where it was made completely clear), since it makes explicit use of super-strong extensionality (I think this is called beta-translation), that is to say, it is a theorem about extensional DTTs/MLTTs.

It’s not even totally clear to me that every intensional type theory actually has an (∞,1)-categorical semantics without the consideration of the univalence axiom. I would make this clearer, but I am really out of my depth with type theories, so I’m just alerting you to the fact that this is stated confusingly

*almost everywhere*(the only place where it’s clear is in the page on identity types).

- Discussion Type
- discussion topicPreduals
- Category Latest Changes
- Started by TobyBartels
- Comments 9
- Last comment by TobyBartels
- Last Active Aug 6th 2012

Not much here, but: predual.

- Discussion Type
- discussion topicInclusion-exclusion
- Category Latest Changes
- Started by TobyBartels
- Comments 5
- Last comment by Mike Shulman
- Last Active Aug 6th 2012

New page: inclusion-exclusion principle

- Discussion Type
- discussion topicDuals
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Aug 6th 2012

- Discussion Type
- discussion topicPaul-André Melliès
- Category Latest Changes
- Started by Tim_Porter
- Comments 7
- Last comment by TobyBartels
- Last Active Aug 5th 2012

We ended up with two entries on Paul-André Melliès. One did not have the hyphen. I did a redirect to the older one which has the hyphenation.

- Discussion Type
- discussion topicmonomorphism in an (oo,1)-category
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Mike Shulman
- Last Active Aug 5th 2012

- Discussion Type
- discussion topicPositive cones.
- Category Latest Changes
- Started by TobyBartels
- Comments 26
- Last comment by TobyBartels
- Last Active Aug 5th 2012

New page: positive cone, including the extended positive cone of a

*W*^{*}-module.

- Discussion Type
- discussion topicLambert W function
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by TobyBartels
- Last Active Aug 2nd 2012

Wrote Lambert W function. It was an excuse to record Joyal’s proof of Cayley’s theorem on the number of tree structures one can put on an $n$-element set (which is $n^{n-2}$).

- Discussion Type
- discussion topiciterated monoidal category
- Category Latest Changes
- Started by Todd_Trimble
- Comments 1
- Last comment by Todd_Trimble
- Last Active Aug 1st 2012

I’ve been inactive here for some months now; I hope this will significantly change soon.

I have written a stubby beginning of iterated monoidal category, with what is admittedly a conjectural definition that aims to be slick. I am curious whether anyone can help me with the following questions:

Is the definition correct (i.e., does it unpack to the usual definition)? If so, is there a good reference for that fact?

Assuming the definition is correct, it hinges on the notion of

*normal*lax homomorphism (between pseudomonoids in a 2-category with 2-products). Why the normality?

In other words (again assuming throughout that the definition is correct), it would seem natural to consider the following type of iteration. Start with any 2-category with 2-products $C$, and form a new 2-category with 2-products $Mon(C)$ whose 0-cells are pseudomonoids in $C$, whose 1-cells are lax homomorphisms (with no normality condition, viz. the condition that the lax constraint connecting the units is an isomorphism), and whose 2-cells are lax transformations between lax homomorphisms. Then iterate $Mon(-)$, starting with $C = Cat$. Why isn’t this the “right” notion of iterated monoidal category, or in other words, why do Balteanu, Fiedorowicz, Schwänzel, and Vogt in essence replace $Mon(-)$ with $Mon_{norm}(-)$ (where all the units are forced to coincide up to isomorphism)?

Apologies if these are naive questions; I am not very familiar with the literature.

- Discussion Type
- discussion topicExcision
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Jul 30th 2012

I created a stub on excision, but this is just a link to the Wikipedia page for the moment.

- Discussion Type
- discussion topicConcrete and abstract structures.
- Category Latest Changes
- Started by TobyBartels
- Comments 4
- Last comment by Mirco Richter
- Last Active Jul 28th 2012

Concrete, abstract: group actions, groups; concrete categories, categories; Cartesian spaces, vector spaces; von Neumann algebras, $W^*$-alebras; material sets, structural sets; etc. At concrete structure.

- Discussion Type
- discussion topiccategory with star-morphisms
- Category Latest Changes
- Started by porton
- Comments 16
- Last comment by porton
- Last Active Jul 26th 2012

- I've added the following two new (related) pages to nLab wiki:

category with star-morphisms

abrupt category

These concept aroused in my research of what I call cross-composition product (a stub in the wiki).

See my research, especially this manuscript for details and examples.

- Discussion Type
- discussion topicoverview over group schemes
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 1
- Last comment by Stephan A Spahn
- Last Active Jul 21st 2012

I wrote an overview over some constructions on- and examples of group schemes.

- Discussion Type
- discussion topicnotes from String-Math 2012
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 21st 2012

as some of you will have seen, I had spent part of the last week with attending talks at

*String-Math 2012*and posting some notes about these, to the $n$Café (here). For many of these notes I added material to existing $n$Lab entries (mostly just references) or created $n$Lab entries (mostly just stubs).But since at the same time I was also finalizing the writup of an article as well as doing yet some other things, the whole undertaking was a bit time-pressured. As a result, I decided it would be too much to announce every single $n$Lab edit that I did here on the $n$Forum.

So I ask you for understaning that hereby I just collectively announce these edits here: those who care should please scan through the list of blue links here and see if they spot pointers to $n$Lab entries where they would like to check out the recent edits.

I think I can guarantee, though, that in all cases I did edits that should be entirely uncontroversial, their main defect being that in many cases they leave one wish for more exhaustive discussion.

- Discussion Type
- discussion topiccategorification in representation theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 17th 2012

added some references by Catahrina Stroppel at the end of

*categorification in representation theory*(also added the words “representation theory” to the entry itself :-)

- Discussion Type
- discussion topicNew page: [[structured set]]
- Category Latest Changes
- Started by TobyBartels
- Comments 4
- Last comment by TobyBartels
- Last Active Jul 16th 2012

I've been meaning to write this for a while. Now I need to look at Bourbaki this weekend to explain their approach.

- Discussion Type
- discussion topicTowards QFT
- Category Latest Changes
- Started by fpaugam
- Comments 2
- Last comment by TobyBartels
- Last Active Jul 15th 2012

- Hi guys,

The situation with my habilitation has been resolved.

I decided to postone it to more favourable times.

You can refer to my book and link it.

Best,

Frédéric

- Discussion Type
- discussion topicRadon–Nikodym derivatives.
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by hilbertthm90
- Last Active Jul 14th 2012

New page: Radon–Nikodym derivative.

- Discussion Type
- discussion topicPure and mixed states.
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by TobyBartels
- Last Active Jul 14th 2012

I moved some material from state to create pure state (redirect from mixed state).

- Discussion Type
- discussion topicquantum affine algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 13th 2012

I have created a stub

*quantum affine algebra*as a means to collect some references, alluded to here.If there is any expert on the matter around, he or she should please feel invited to add an illuminating Idea-section to the entry.

- Discussion Type
- discussion topiccalculus, types and trees
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 10
- Last comment by Mike Shulman
- Last Active Jul 12th 2012

I created types and calculus and seven trees in one. Both entries as yet contain just references.

It would be nice to have more articles expanding on the reltion of calculus and (higher) category theory /type theory.

- Discussion Type
- discussion topicconjugacy class
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by zskoda
- Last Active Jul 11th 2012

created

*conjugacy class*

- Discussion Type
- discussion topicmetaplectic representation
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Urs
- Last Active Jul 11th 2012

New stub metaplectic representation, for now containing only some references.

- Discussion Type
- discussion topicdiagram of LCTVS properties
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 10th 2012

Maybe I am not searching correctly, but it seems to me that until 2 minutes ago the rather remarkable

*diagram of LCTVS properties*was linked to from exactly none non-meta $n$Lab page. It was effectively invisble unless one explicitly searched for “SVG”.Let me know if there is a reason for it remaining invisible. Assuming that there isn’t, I have now added it to

*locally convex space*and to*functional analysis - contents*(which I restructured slightly, moving the*two*such overview diagrams prominently to the top, where they can be recognized as what they are).

- Discussion Type
- discussion topicmetaplectic structure
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Jul 10th 2012

stub for

*metaplectic structure*