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- Discussion Type
- discussion topiccomparison theorem (étale cohomology)
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Nov 22nd 2013

brief note

*comparison theorem (étale cohomology)*

- Discussion Type
- discussion topiccomplex analytic topology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 22nd 2013

brief entry

*complex analytic topology*, just for completeness

- Discussion Type
- discussion topicspectrum disambiguation
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 21st 2013

we had an entry

*spectrum (geometry)*which wasn’t linked to from almost anywhere, in particular not from*spectrum - disambiguation*.I have now added a bunch of cross-links, between these two entries and between the entries that they link to. It’s better now than it was before, but could still do with further improvement.

- Discussion Type
- discussion topicprofinite space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 20th 2013

the entry profinite space and entries related to it were/are a bit in need of some care.

The entry used to start out saying “Profinite space is another word for Stone space”, which was misleading, because there is a not-entirely-trivial equivalence involved. So I changed it to

A

*profinite set*is a pro-object in FinSet. By Stone duality these are equivalent to Stone spaces and thus are often called*profinite spaces*. So these are compact Hausdorff totally disconnected topological spaces.Also cross-links with profinite reflection were missing, and so I added them. Also cross-linked with

*finite set*, with*localic reflection*and maybe with more.The entry profinite space is still stubby/unsatisfactory.

- Discussion Type
- discussion topicpro-étale cohomology
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Nov 20th 2013

started entries

Question: We have the implications

étale morphism $\Rightarrow$ weakly étale morphism $\Rightarrow$ formally étale morphism

but can one say more specifically what kind of generalized finite presentability condition makes a formally étale morphism a weakly étale morphism?

- Discussion Type
- discussion topicLoday
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Nov 20th 2013

I have fixed some dead links relating to Loday which were occurring n several pages.

- Discussion Type
- discussion topicatoms in cohesion
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 19th 2013

made a note of a simple observation:

for $X$ an atom in a cohesive $\infty$-topos $\mathbf{H}$ over $\infty Grpd$, then also the slice $\mathbf{H}_{/X}$ is cohesive … except possibly for the property that shape preserves binary products (but it does preserve the terminal object):

- Discussion Type
- discussion topicchromatic spectral sequence
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 18th 2013

stub for chromatic spectral sequence, so far mainly to record that it arises as the Lurie spectral sequence of the chromatic tower (thanks to Dylan Wilson and Marc Hoyois)

- Discussion Type
- discussion topiccontinuous algebra
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Nov 18th 2013

Created continuous algebra.

- Discussion Type
- discussion topictangent cohesive infinity-topos
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by David_Corfield
- Last Active Nov 18th 2013

now the preprint referred to at

*tangent cohesive (infinity,1)-topos*is out:- Ulrich Bunke, Thomas Nikolaus, Michael Völkl,
*Differential cohomology theories as sheaves of spectra*(arXiv:1311.3188)

- Ulrich Bunke, Thomas Nikolaus, Michael Völkl,

- Discussion Type
- discussion topicgeneralised Eilenberg-MacLane space
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by Tim_Porter
- Last Active Nov 18th 2013

I noted an entry on generalized Eilenberg-MacLane spaces, but note that there is another use of this term in the literature, namely the representing fibrations for cohomology with local coefficients. These are the fibrations used by Gitler and then by Alan Robinson, Hans Baues and others more recently. What would be the preferred name for these latter things. (I personally find the idea of giving a name to products of Eilenberg- Mac Lane spaces other that ‘products of Eilenberg - Mac Lane spaces’ a bit strange, but I know that there is some strange terminology around!)

- Discussion Type
- discussion topiccoinvariant
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Nov 15th 2013

I noticed by accident that we have an entry

*coinvariant*. Then I noticed that we also have an entry*homotopy coinvariant functor*.I have now added cross-links between these entries and with

*invariant*and*orbit*, so that they no longer remain hidden.I also edited the first case of group representation coinvariants at

*coinvariant*a little.

- Discussion Type
- discussion topic"Modern Differential Geometry and Physics"
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 15th 2013

this Physics.SE question made me create a category:reference entry for

- Chris Isham,
*Modern Differential Geometry for Physicists*

- Chris Isham,

- Discussion Type
- discussion topicbrave new Hopf algebroids
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Nov 15th 2013

I noticed that some old entries were requesting a keyword link for

*brave new algebra*, so I created it and filled in a default-paragraph. Please feel invited to expand.In that context I have a question: the dual generlized Steenrod algebras have been called “brave new Hopf algebroids” in articles including

Andrew Baker,

*Brave new Hopf algebroids*(pdf)Andrew Baker and Alain Jeanneret,

*Brave new Hopf algebroids and extensions of $MU$-algebras*, Homology Homotopy Appl. Volume 4, Number 1 (2002), 163-173. (Euclid)Mark Hovey,

*Homotopy theory of comodules over a Hopf algebroid*(arXiv:math/0301229)

But the Hopf algebroids considered in these articles are ordinary Hopf algebroids, they are given not by Hopf $\infty$-algebras $(E, E \wedge E)$ but by their homotopy groups $(E_\bullet, E_\bullet(E))$, unless I am missing something.

So at least without further discussion, calling $(E_\bullet, E_\bullet(E))$ “brave new” is a bit of a stretch. The brave new thing would be $(E, E \wedge E)$ (if indeed it is a “Hopf $\infty$-algebroid”).

Can anyone say more about this? I can’t seem to find any source talking about this. The canonical guess of googling for “derived Hopf algebroid” doesn’t show relevant results.

- Discussion Type
- discussion topicLandweber-Novikov theorem
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Nov 15th 2013

created

*Landweber-Novikov theorem*

- Discussion Type
- discussion topicmotives in physics
- Category Latest Changes
- Started by Urs
- Comments 29
- Last comment by Urs
- Last Active Nov 14th 2013

started

*motives in physics*with text that I posted as an answer to this Physics.SE question.Needs to be polished and expanded. But I have to run now.

- Discussion Type
- discussion topicQuillen's theorem on MU
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 14th 2013

since it appears in several entries and probably more to come, I gave it an entry of its own:

*Quillen’s theorem on MU*also gave an entry to

*Lazard’s theorem*

- Discussion Type
- discussion topicfinite spectrum
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 13th 2013

I needed

*finite spectrum*To be able to conveniently link I have also splitt of

*finite CW-complex*from*CW-complex*

- Discussion Type
- discussion topicLubin-Tate theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 13th 2013

some basics at

*Lubin-Tate theory*(wanted to do more, but the nLab is giving me a really hard (down-)time )

- Discussion Type
- discussion topicimage of J -- table
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by David_Corfield
- Last Active Nov 13th 2013

created a table-for-inclusion

*image of J – table*listing pertinent information in low degree, and included it in some relevant entries

- Discussion Type
- discussion topicMorava E-theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 13th 2013

started a very stubby

along with very stubby

and a very stubby

Had wanted to do more, but now I am running out of steam. Maybe the stubs inspire somebody to add a little more…

- Discussion Type
- discussion topicBousfield equivalence
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 13th 2013

created a brief entry for

*Bousfield equivalence*

- Discussion Type
- discussion topiccontact geometry
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Nov 13th 2013

I messed up slightly: i had forgotten that there was already a stub titled

*contact geometry*. Now I have created*contact manifold*with some content that might better be at*contact geometry*. I should fix this. But not right now.

- Discussion Type
- discussion topicEinstein's equation
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 13th 2013

created Einstein’s equation, only to record a writeup by Gonzalo Reyes which I just came across by chance, who gives a discussion in terms of synthetic differential geometry.

- Discussion Type
- discussion topicphantom map
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 13th 2013

quick entry for

*phantom map*

- Discussion Type
- discussion topicchromatic convergence theorem
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 12th 2013

brief Idea-section at

*chromatic convergence theorem*

- Discussion Type
- discussion topictelescopic localization
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 12th 2013

stub for

*telescopic localization*,

- Discussion Type
- discussion topic"Chromatic Homotopy Theory"
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 12th 2013

finally created the category:reference-entry for Lurie’s chromatic lecture. See

*Chromatic Homotopy Theory*(And as a special service to the community… with lecture titles. ;-)

Lecture 1

*Introduction*(pdf)Lecture 2

*Lazard’s theorem*(pdf)Lecture 3

*Lazard’s theorem (continued)*(pdf)Lecture 4

*Complex-oriented cohomology theories*(pdf)Lecture 5

*Complex bordism*(pdf)Lecture 6

*MU and complex orientations*(pdf)Lecture 7

*The homology of MU*(pdf)Lecture 8

*The Adams spectral sequence*(pdf)Lecture 9

*The Adams spectral sequence for MU*(pdf)Lecture 10

*The proof of Quillen’s theorem*(pdf)Lecture 11

*Formal groups*(pdf)Lecture 12

*Heights and formal groups*(pdf)Lecture 13

*The stratification of $\mathcal{M}_{FG}$*(pdf)Lecture 14

*Classification of formal groups*(pdf)Lecture 15

*Flat modules over $\mathcal{M}_{FG}$*(pdf)Lecture 16

*The Landweber exact functor theorem*(pdf)Lecture 17

*Phanton maps*(pdf)Lecture 18

*Even periodic cohomology theories*(pdf)Lecture 19

*Morava stabilizer groups*(pdf)Lecture 20

*Bousfield localization*(pdf)Lecture 21

*Lubin-Tate theory*(pdf)Lecture 22

*Morava E-theory and Morava K-theory*(pdf)Lecture 23

*The Bousfield Classes of $E(n)$ and $K(n)$*(pdf)Lecture 24

*Uniqueness of Morava K-theory*(pdf)Lecture 25

*The Nilpotence lemma*(pdf)Lecture 26

*Thick subcategories*(pdf)Lecture 27

*The periodicity theorem*(pdf)Lecture 28

*Telescopic localization*(pdf)Lecture 29

*Telescopic vs $E_n$-localization*(pdf)Lecture 30

*Localizations and the Adams-Novikov spectral sequence*(pdf)Lecture 31

*The smash product theorem*(pdf)Lecture 32

*The chromatic convergence theorem*(pdf)Lecture 33

*Complex bordism and $E(n)$-localization*(pdf)Lecture 34

*Monochromatic layers*(pdf)Lecture 35

*The image of $J$*(pdf)

- Discussion Type
- discussion topiccluster decomposition
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 12th 2013

created a stub for

*cluster decomposition*, since I wanted the link elsewhere, but nothing there yet…

- Discussion Type
- discussion topicBol loop
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Nov 11th 2013

I recently created entry Bol loop. Now I made some corrections and treated the notion of a

**core**of a right Bol loop (the term coming allegedly from Russian term сердцевина).

- Discussion Type
- discussion topicspectral geometry
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active Nov 11th 2013

created a disambiguation page:

*spectral geometry*

- Discussion Type
- discussion topicTychonoff spaces
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by Urs
- Last Active Nov 11th 2013

New article: Tychonoff space.

- Discussion Type
- discussion topicNoncommutative Geometry, Quantum Fields and Motives
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 8th 2013

I gave the book

- Connes, Marcolli,
*Noncommutative Geometry, Quantum Fields and Motives*

a category:reference entry and linked to it from a few relevant entries.

- Connes, Marcolli,

- Discussion Type
- discussion topicE-∞ geometry
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 8th 2013

started stubs

*E-∞ geometry*,*E-∞ scheme*.To be filled with more content, for the moment I just need to be able to use the links.

- Discussion Type
- discussion topichigher chromatic Chern character
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 6th 2013

I am starting entries

for the moment mostly to collect some references. But not much there yet. But if anyone can provide furher hints, that would be welcome.

- Discussion Type
- discussion topicquantization of loop groups
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 6th 2013

have split-off

*quantization of loop groups*from*loop group*

- Discussion Type
- discussion topicA Survey of Eilliptic Cohomology - the derived moduli stack of derived elliptic curves
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Nov 6th 2013

- Discussion Type
- discussion topicA Survey of Elliptic Cohomology - elliptic curves
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Nov 6th 2013

created A Survey of Elliptic Cohomology - elliptic curves with seminar notes on an exposition on elliptic curves.

Am hoping that some kind soul will eventually further go through these seminar notes and copy bits of material to separete entries, where it belongs. Eventually.

- Discussion Type
- discussion topicnear-ring
- Category Latest Changes
- Started by Mike Shulman
- Comments 6
- Last comment by zskoda
- Last Active Nov 5th 2013

- Discussion Type
- discussion topicaffine modality
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 4th 2013

have created

*affine modality*

- Discussion Type
- discussion topicdouble negation modality / (-1)-truncation modality
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Mike Shulman
- Last Active Nov 4th 2013

I have created a stub for

*n-truncation modality*and cross-linked with*double negation modality*.I gather that double negation = (-1)-truncation in a “predicative context”, but maybe I don’t fully understand yet what predicativity has to do with it.

- Discussion Type
- discussion topicAdams-Novikov spectral sequence
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 4th 2013

I have added some more informative Idea-sentences to

*Adams spectral sequence*and to*Adams-Novikov spectral sequence*. Also added more references.

- Discussion Type
- discussion topicfraction
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 4th 2013

felt like the nLab should have an entry

*fraction*

- Discussion Type
- discussion topicstable unitary group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 4th 2013

have split off an entry

*stable unitary group*from the material at*topological K-theory*

- Discussion Type
- discussion topicstable orthogonal group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 4th 2013

added the “song of stable homotopy groups” to

*stable orthogonal group*

- Discussion Type
- discussion topicChanges to 'Banach algebra' page
- Category Latest Changes
- Started by Yemon Choi
- Comments 5
- Last comment by Todd_Trimble
- Last Active Nov 4th 2013

Popped my head round the door and made a couple of changes to Banach algebra

The first change was to attempt a more lax position on what should constitute a Banach coalgebra: only looking at comonoids in the monoidal category of Banach spaces (geometric or topogical) with projective tensor product would rule out several important examples that have arisen in e.g. abstract harmonic analysis. The existence of different monoidal structures in the category of Banach spaces is a pain, but without it one would miss out on a rich world of examples.

The second was to add, to the list of examples, the celebrated-in-my-world-and-possibly-no-others Arens products on the double dual of a Banach algebra. I’ve made a stab at linking them to the related concepts of tensorial strength and strong monad but would welcome feedback or improvements.

- Discussion Type
- discussion topicsynthetic projective geometry
- Category Latest Changes
- Started by zskoda
- Comments 7
- Last comment by zskoda
- Last Active Nov 3rd 2013

New entry synthetic projective geometry and also sort of disambiguation and history page synthetic geometry making a distinction with synthetic differential geometry.

- Discussion Type
- discussion topicStephen Gaito, cardinal number
- Category Latest Changes
- Started by TobyBartels
- Comments 5
- Last comment by Todd_Trimble
- Last Active Nov 3rd 2013

Stephen Gaito has joined with a question at cardinal number. I tried to reply.

- Discussion Type
- discussion topicisotopy, isotope
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Nov 2nd 2013

isotope (physics) and isotope (algebra) with redirect for isotopy (algebra). I have read and thought much about isotopies in last couple of weeks, but no time at this point to write much about it into $n$Lab.

- Discussion Type
- discussion topicBruck-Toyoda theorem
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Nov 2nd 2013

- Discussion Type
- discussion topicRiehl-Verity
- Category Latest Changes
- Started by DavidRoberts
- Comments 2
- Last comment by Urs
- Last Active Nov 2nd 2013

Added references to the recent Riehl-Verity papers to quasi-category, adjoint (infinity,1)-functor and monadicity theorem. Any more places it should go?

- Discussion Type
- discussion topicWeil conjecture
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Nov 1st 2013

started

*Weil conjecture*

- Discussion Type
- discussion topicsemisimple category
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by TobyBartels
- Last Active Nov 1st 2013

Chris Schommer-Pries posted a question/suggestion in the query box at semisimple category

- Discussion Type
- discussion topicSchubert calculus
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Oct 31st 2013

have added to the Idea-section at

*Schubert calculus*the following paragraph:Schubert calculus is concerned with the ring structure on the cohomology of flag varieties and Schubert varieties. Traditionally this was considered for ordinary cohomology (see References – traditional) later also for generalized cohomology theories (see References – In generalized cohomology), notably in complex oriented cohomology theory such as K-theory, elliptic cohomology and algebraic cobordism.

And have added references on Schubert calculus for generalized cohomology.

- Discussion Type
- discussion topicHomotopy topoi and equivariant elliptic cohomology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 31st 2013

I gave the following an category:reference-entry

- David Gepner,
*Homotopy topoi and equivariant elliptic cohomology*, 2005

and linked to it from various relevant entries.

- David Gepner,

- Discussion Type
- discussion topicreductive group
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 30th 2013

stub for reductive group

- Discussion Type
- discussion topicThe norm of the identity element in a unital Banach algebra …
- Category Latest Changes
- Started by TobyBartels
- Comments 7
- Last comment by Yemon Choi
- Last Active Oct 30th 2013

… need not be $1$, but it shouldn't be larger; remarks about this are now at Banach algebra (and also at JB-algebra).

- Discussion Type
- discussion topicKac character formula
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 30th 2013

stub for

*Kac character formula*, for the moment just so as to record the citations.

- Discussion Type
- discussion topicEssentially bounded functions
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 29th 2013

We don't actually need essentially bounded functions as such, since measurable functions should only be almost-everywhere defined by default, but there they are.

- Discussion Type
- discussion topicFinite dimensions
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 28th 2013

There is a deliberately ambiguous stub at finite-dimensional space.

We might collect there all of the nice things about finite-dimensional spaces (for various notions of ’space’).