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- Discussion Type
- discussion topicLawvere's definition of adjoint functors
- Category Latest Changes
- Started by Colin Zwanziger
- Comments 10
- Last comment by Mike Shulman
- Last Active Jul 28th 2014

I added a section on Lawvere’s definition to adjoint functor and also made an article for Functorial Semantics of Algebraic Theories.

- Discussion Type
- discussion topicmod p Whitehead theorem
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 25th 2014

created some bare minimum at

*mod p Whitehead theorem*

- Discussion Type
- discussion topicp-adic geometry, homotopy, cohomology, physics
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Urs
- Last Active Jul 25th 2014

created stub for

with just some references and

with just some pointers, cross-linked with

To be expanded…

- Discussion Type
- discussion topicp-localization
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Jul 24th 2014

I suppose we were lacking an entry on

*p-localization*(?)

- Discussion Type
- discussion topicWitt vectors
- Category Latest Changes
- Started by hilbertthm90
- Comments 17
- Last comment by David_Corfield
- Last Active Jul 24th 2014

I’ve created a page for the Witt vectors. It seems that even with all that I wrote here (don’t worry I had a set of about 10 blog entries I wrote a few months ago that I just condensed, so I didn’t write this whole thing tonight) there are all sorts of things still missing here. The Witt functor is mention at Lambda-ring and there seems to be connections to the field with one element (?!). I just needed to refer to Witt vectors in the next few pages I want to make, so I decided this had to come first. Dieudonne module will need it and obviously Witt cohomology will need it.

- Discussion Type
- discussion topicétale topos
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Urs
- Last Active Jul 23rd 2014

added to

*étale topos*some basics in the section*Properties – Base change and sheaf cohomology*

- Discussion Type
- discussion topicspam
- Category Latest Changes
- Started by Urs
- Comments 58
- Last comment by TobyBartels
- Last Active Jul 23rd 2014

killed a spam page, now called spam

- Discussion Type
- discussion topicinfinitesimal and local - table
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 23rd 2014

I felt like starting a table

*infinitesimal and local - table*and included it into the relevant entries. So far it reads as follows:first order infinitesimal object infinitesimal $\subset$ formal = arbitrary order infinitesimal $\subset$ local = stalkwise $\subset$ finite derivative Taylor series germ function tangent vector jet germ of curve curve Lie algebra formal group local Lie group Lie group Poisson manifold formal deformation quantization local strict deformation quantization strict deformation quantization Can be further expanded, clearly.

- Discussion Type
- discussion topicBorel-Weil theorem
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by noud
- Last Active Jul 23rd 2014

The entry

*Borel-Weil theorem*mentions extensions of the theorem to quantum groups, without however giving a reference. I just got an email asking for these.The statement dates from August 19, 2009, due to Zoran.

- Discussion Type
- discussion topicbranched cover of Riemann sphere
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Todd_Trimble
- Last Active Jul 22nd 2014

created a bare minimum at

*branched cover of Riemann sphere*, just to record the fact that every compact connected Riemann surface admits this structure.

- Discussion Type
- discussion topicTransfinite constructions of free algebras
- Category Latest Changes
- Started by Fosco
- Comments 6
- Last comment by Dmitri Pavlov
- Last Active Jul 22nd 2014

I began adding proofs of Lemma 1-4 to the page transfinite construction of free algebras. The layout of the two array environment has to be fixed; proof of 3-4 to be added.

Any help/suggestion is extremely appreciated!

- Discussion Type
- discussion topicp-adic complex number
- Category Latest Changes
- Started by Urs
- Comments 38
- Last comment by Urs
- Last Active Jul 22nd 2014

gave

*p-adic complex numbers*an entry

- Discussion Type
- discussion topicfinite dim vector spaces
- Category Latest Changes
- Started by Tim_Porter
- Comments 8
- Last comment by Tim_Porter
- Last Active Jul 21st 2014

Someone (anonymous) has created an empty page oon finite dimensional vector spaces.

- Discussion Type
- discussion topicglobal field
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by David_Corfield
- Last Active Jul 21st 2014

created a minimum at

*global field*

- Discussion Type
- discussion topicrestricted product
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Jul 20th 2014

needed to point to

*restricted product*, so I created a bare (and unsophisticated) minimum

- Discussion Type
- discussion topicImaginary numbers
- Category Latest Changes
- Started by TobyBartels
- Comments 14
- Last comment by Todd_Trimble
- Last Active Jul 20th 2014

I mostly wanted to record the correct meaning of this term. Then maybe later I can use this as a reference to fix Wikipedia (^_^). But there's a bit more here too.

- Discussion Type
- discussion topicCartesian space
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Colin Tan
- Last Active Jul 20th 2014

gave Cartesian space a TOC and added some statements and references.

- Discussion Type
- discussion topicBiholomorphic function
- Category Latest Changes
- Started by Colin Tan
- Comments 8
- Last comment by Colin Tan
- Last Active Jul 20th 2014

Edited biholomorphic function to follow the same format as diffeomorphism. In particular, this means that I qualified biholomorphic function to refer only to maps between complex manifolds. Is there a more general definition of holomorphic functions between complex analytic spaces?

- Discussion Type
- discussion topicformal disk
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 19th 2014

created

*formal disk*with some default text, just so that the links from*function field analogy – table*point to something

- Discussion Type
- discussion topicp-adic number
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Jul 18th 2014

the entry

*p-adic number*had (and has) its Definition-section filled with a lengthy recollection of the*p-adic integers*. I have split into two subsections, such as to make it more clear where the actual definition begins.

- Discussion Type
- discussion topicTate's acyclicity theorem
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 18th 2014

created a minimum at

*Tate’s acyclicity theorem*. Also created a minimum at*Banach module*.

- Discussion Type
- discussion topicquasi-net
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 18th 2014

in non-archimedean analytic geometry there is a standard concept of

*quasi-net*used notably in the definition of Berkovich analytic spaces.I have created a minumum entry on this, in the course of creating a bunch of non-archimedean analytic entries. But clearly this needs some comment on terminology. Help is welcome.

- Discussion Type
- discussion topicreal space
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jul 17th 2014

started

*real space*(of course that may eventually want to be disambiguated, but maybe for the moment it’s okay)

- Discussion Type
- discussion topicstructures in a cohesive (oo,1)-topos
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jul 17th 2014

I worked a bit on bringing the list of structures present in a cohesive (oo,1)-topos into shape, expanding it and filling in details. See the table of contents at cohesive (infinity,1)-topos.

- Discussion Type
- discussion topicComplex numbers
- Category Latest Changes
- Started by Colin Tan
- Comments 1
- Last comment by Colin Tan
- Last Active Jul 17th 2014

Added some more (basic) information on complex conjugation to complex numbers.

- Discussion Type
- discussion topicmoduli space of curves/of Riemann surfaces
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active Jul 16th 2014

added to

*moduli space of curves*a paragraph mentioning the result by Harer-Zagier on the orbifold Euler characteristic of $\mathcal{M}_{g,1}$ being $\zeta(1-2g)$.

- Discussion Type
- discussion topicaugmented Teichmüller space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 16th 2014

created some minimum at

*augmented Teichmüller space*.I have also touched

*moduli stack of curves*and*Teichmüller space*and*Deligne-Mumford compactification*adding references and various little pointers etc.

- Discussion Type
- discussion topicétale groupoid
- Category Latest Changes
- Started by Urs
- Comments 79
- Last comment by zskoda
- Last Active Jul 15th 2014

I have touched étale groupoid and various entries related to this.

I have made

*orbit space*redirect to orbit, though eventually it might want to be a separate entry.Also I have made

*foliation theory*redirect to folitation, though eventually it might want to be a separate entry.I have added Deligne-Mumford stack as a “related concept” to étale groupoid, though eventually what I am after is a complex of entries that discusses approaches to a general notion of étale ∞-groupoids and how these sub-entries fit into a more general story.

So I’ll be creating a stub étale ∞-groupoid, but I am not sure if I have time and energy to have it be more than a reminder for things to look into later.

- Discussion Type
- discussion topicBanach ring
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by TobyBartels
- Last Active Jul 15th 2014

started to split off

*Banach ring*from*Banach algebra*. But need to interrupt now.

- Discussion Type
- discussion topicDonaldson-Uhlenbeck-Yau theorem
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 14th 2014

started some minimum at

*Donaldson-Uhlenbeck-Yau theorem*

- Discussion Type
- discussion topicGIT-stable point
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 14th 2014

The relation between slope-(semi-)stability of vector bundles and the general concept of (semi-)stability in the sense of geometric invariant theory seems to be a well-kept secret as far as expositions and lecture notes etc. go. One place where I see a genuine review of this relation is

- Alfonso Zamora Saiz,
*On the stability of vector bundles*, Master thesis 2009 (pdf)

I have created an entry

(with a bunch of variant terms redirecting to it) that is presently just a glorified pointer to the relevant pages in this thesis. Then I have added related comments to the existing entries

- Alfonso Zamora Saiz,

- Discussion Type
- discussion topicBeilinson conjectures
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 14th 2014

might anyone have an electronic copy of the English version of Brylinski-Zucker 91 “An overview of recent advances in Hodge theory”?

- Discussion Type
- discussion topicnormed field
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 13th 2014

have added to

*normed field*the statement that if the product preserves the norm strictly (by equality, not just by inequality) then one speaks of a “valued field”.

- Discussion Type
- discussion topicLinear logic
- Category Latest Changes
- Started by TobyBartels
- Comments 58
- Last comment by Urs
- Last Active Jul 12th 2014

I put a complete definition at linear logic.

- Discussion Type
- discussion topicGromov-Witten theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by adeelkh
- Last Active Jul 12th 2014

added to

*Gromov-Witten theory*and to*orbifold*pointers relating to Ruan et al.’s work on orbifold GW theory

- Discussion Type
- discussion topicobject classifier
- Category Latest Changes
- Started by Thomas Holder
- Comments 7
- Last comment by Thomas Holder
- Last Active Jul 12th 2014

As I’ve added some material to classifying topos of the theory of objects, I’ve done some rewriting as well. Feel free to rectify!

- Discussion Type
- discussion topicwalking structures
- Category Latest Changes
- Started by Mike Shulman
- Comments 66
- Last comment by Todd_Trimble
- Last Active Jul 8th 2014

I created the page walking structure. I’m open to better names for it. It also probably needs to be linked from a bunch of different places.

- Discussion Type
- discussion topicsheaf of rational functions
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jul 7th 2014

should say that yesterday, right before my battery died, I had started a bare minimum at

*sheaf of rational functions*, just so as to complete the corresponding entry at*function field analogy – table*

- Discussion Type
- discussion topicreal analytic space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 6th 2014

added to

*real analytic space*the statement and reasoning of Whitneys’s theorem (unformatted for the moment, am in a rush)

- Discussion Type
- discussion topicgeometric Langlands QFT -- table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 2nd 2014

started a table-for-inclusion

and included it into relevant entries. (But it’s still tiny at the moment.) Also started a bunch of stubs needed for this, such as

*Hecke correspondence*,*Hecke transform*,*Hecke eigensheaf*,*electric eigenbrane*,*magnetic eigenbrane*.Neither of these have much content yet apart from a lightning Idea-section, a pointer to some literature and cross-links.

- Discussion Type
- discussion topic’t Hooft operator
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 2nd 2014

started some minimum at

*’t Hooft operator*

- Discussion Type
- discussion topicform of an algebraic group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 2nd 2014

put something basic into

*form of an algebraic group*

- Discussion Type
- discussion topiclogarithmic geometry
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 1st 2014

have added some more references to

*logarithmic geometry*and cross-linked a bit. (but there is still no genuine content)

- Discussion Type
- discussion topiccombinatorial model category
- Category Latest Changes
- Started by ilanbarnea
- Comments 6
- Last comment by ilanbarnea
- Last Active Jun 30th 2014

- I have deleted a sentence that is not correct. See the last discussion on cellular model category.

By the way, how do you sign in to nLab. I am signed in to the forum but when I edited it was shown as anonymous coward...

- Discussion Type
- discussion topicBousfield localization of model categories
- Category Latest Changes
- Started by ilanbarnea
- Comments 3
- Last comment by Urs
- Last Active Jun 30th 2014

- I have deleted some sentences that are not correct. See the last discussion on cellular model category.

- Discussion Type
- discussion topicsmall object
- Category Latest Changes
- Started by ilanbarnea
- Comments 3
- Last comment by Urs
- Last Active Jun 30th 2014

- I have deleted some statements that are not correct. It is quite obvious that what I have deleted is wrong, in fact the restatement given a few lines later is the verification of the condition that that map is onto (which is definitely not automatic).

- Discussion Type
- discussion topicp-local module
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Jun 25th 2014

Created p-local module.

- Discussion Type
- discussion topicanalytification
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Marc Hoyois
- Last Active Jun 24th 2014

started a minimum at

*analytification*, mainly interested for the moment in collecting the references now given there which discuss analytification of algebraic (etc.) stacks

- Discussion Type
- discussion topicalmost complex structure
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Colin Tan
- Last Active Jun 21st 2014

slightly expanded and prettified a bit at

*almost complex structure*(nothing non-trivial, just cosmetics)

- Discussion Type
- discussion topicKR-theory
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Colin Tan
- Last Active Jun 21st 2014

I have expanded just a little at

*KR-theory*by giving it an actual Idea-paragraph and adding some more references.

- Discussion Type
- discussion topicrelation between compact Lie groups and reductive algebraic groups
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 20th 2014

I gather (via this nice MO comment) that

The functor that takes linear algebraic groups $G$ to their $\mathbb{R}$-points $G(\mathbb{R})$ constitutes an equivalence of categories between compact Lie groups and $\mathbb{R}$-aniosotropic reductive algebraic groups over $\mathbb{R}$ all whose connected components have $\mathbb{R}$-points.

For $G$ as in this equivalence, then then complex Lie group $G(\mathbb{C})$ is the complexification of $G(\mathbb{R})$.

I have a gap in my education here and would like to fill it. What’s a good source that discusses this statement a bit more? And which one of Chevalley’s articles is this result originally due?

- Discussion Type
- discussion topicp-convex polarization
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 17th 2014

started a minimum at

*p-convex polarization*

- Discussion Type
- discussion topicabsolute Galois group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 16th 2014

added to

*absolute Galois group*and to*Grothendieck-Teichmüller group*brief pointers for the inclusion of the former into the latter (for the case of the rationals) and a pointer to- Jakob Stix,
*The Grothendieck-Teichmüller group and Galois theory of the rational numbers*, 2004 (pdf)

- Jakob Stix,

- Discussion Type
- discussion topicseparable closure
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 16th 2014

I noticed tha tthe entry

*separable closure*existed but was effectively devoid of content. I have now copy-and-pasted the relevant paragraphs from the entry*Galois theory*into it.

- Discussion Type
- discussion topicFrölicher spectral sequence
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 16th 2014

Have given

*Frölicher spectral sequence*an Idea-paragraph and some pointers, but it is still a stub.

- Discussion Type
- discussion topicThe Mathematical Literature
- Category Latest Changes
- Started by andreas
- Comments 10
- Last comment by zskoda
- Last Active Jun 15th 2014

I created this page: http://ncatlab.org/nlab/show/The+Mathematical+Literature

Am I right that I’m supposed to post about this here at the nForum? How big should an edit be in order to deserve a post here?

And can i link from the nForum to the nLab by doing this? The+Mathematical+Literature

- Discussion Type
- discussion topicThe empty group
- Category Latest Changes
- Started by TobyBartels
- Comments 10
- Last comment by TobyBartels
- Last Active Jun 15th 2014

I wrote a bit at heap about the empty heap (and its automorphism group, the empty group, which I put in the headline for maximum shock value).

- Discussion Type
- discussion topicBerkovich space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 12th 2014

added pointers to the section on cohomology.

- Discussion Type
- discussion topicB1-homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by David_Corfield
- Last Active Jun 12th 2014

Over on MO (in the comments here) Stefan Wendt kindly reminds me of an old $n$Lab entry I once started on

*B1-homotopy theory*. Have added a reference and hope to be adding more.

- Discussion Type
- discussion topicHodge cycle
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jun 11th 2014

started

*Hodge cycle*, but my battery is dying right this moment….